RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1: Find the cube roots of each of the following integers:
(i) −125
(ii) −5832
(iii) −2744000
(iv) −753571
(v) −32768

Answer 1: (i) We have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(ii) We have:  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

To find the cube root of 5832, we use the method of unit digits.
Let us consider the number 5832.
The unit digit is 2; therefore the unit digit in the cube root of 5832 will be 8.
After striking out the units, tens and hundreds digits of the given number, we are left with 5.
Now, 1 is the largest number whose cube is less than or equal to 5.
Therefore, the tens digit of the cube root of 5832 is 1. 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(iii) We have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

To find the cube root of 2744000, we use the method of factorisation.

On factorising 2744000 into prime factors, we get:
2744000=2×2×2×2×2×2×5×5×5×7×7×72744000=2×2×2×2×2×2×5×5×5×7×7×7
On grouping the factors in triples of equal factors, we get:
2744000={2×2×2}×{2×2×2}×{5×5×5}×{7×7×7}2744000=2×2×2×2×2×2×5×5×5×7×7×7
It is evident that the prime factors of 2744000 can be grouped into triples of equal factors and no factor is left over.
Now, collect one factor from each triplet and multiply; we get: 
2×2×5×7=1402×2×5×7=140 
This implies that 2744000 is a cube of 140.
Hence, RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(iv) We have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

To find the cube root of 753571, we use the method of unit digits.
Let us consider the number 753571.
The unit digit is 1; therefore the unit digit in the cube root of 753571 will be 1.
After striking out the units, tens and hundreds digits of the given number, we are left with 753.
Now, 9 is the largest number whose cube is less than or equal to 753 (93<753<10393<753<103).
Therefore, the tens digit of the cube root 753571 is 9. 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(v) We have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

To find the cube root of 32768, we use the method of unit digits.
Let us consider the number 32768.
The unit digit is 8; therefore, the unit digit in the cube root of 32768 will be 2.
After striking out the units, tens and hundreds digits of the given number, we are left with 32.
Now, 3 is the largest number whose cube is less than or equal to 32 (33<32<4333<32<43).
Therefore, the tens digit of the cube root 32768 is 3.

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Question 2: Show that:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 2:

(i) LHS =  RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 3×4=12273×643=3×3×33×4×4×43=3×4=12

RHS =  RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=3×4=1227×643=3×3×3×4×4×43=3×3×3×4×4×43=3×4=12

Because LHS is equal to RHS, the equation is true. 

(ii) LHS =   RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =4×9=3664×7293=4×4×4×9×9×93=4×4×4×9×9×93=4×9=36

RHS = RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRevRD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =4×9=36 

Because LHS is equal to RHS, the equation is true. 

(iii) LHS =  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =5×2×3=30 

RHS =  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =5×(2×3)=30 

Because LHS is equal to RHS, the equation is true. 

(iv) LHS =  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev −5×−10=50

RHS =  RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

=5×10=50-1253×-10003=-5×-5×-53×-10×-10×-103=-5×-10=50
Because LHS is equal to RHS, the equation is true. 

Question 3: Find the cube root of each of the following numbers:
(i) 8 × 125
(ii) −1728 × 216
(iii) −27 × 2744
(iv) −729 × −15625

Answer 3: Property:
For any two integers a and b, RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(i) From the above property, we have:  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×5=10

(ii) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (For any positive integer x, RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root using units digit:
Let us consider the number 1728.
The unit digit is 8; therefore, the unit digit in the cube root of 1728 will be 2.
After striking out the units, tens and hundreds digits of the given number, we are left with 1.
Now, 1 is the largest number whose cube is less than or equal to 1.
Therefore, the tens digit of the cube root of 1728 is 1. 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =12

On factorising 216 into prime factors, we get:
216=2×2×2×3×3×3216=2×2×2×3×3×3
On grouping the factors in triples of equal factors, we get:
216={2×2×2}×{3×3×3}216=2×2×2×3×3×3
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 2×3 = 6

Thus 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =12×6=72 

(iii) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (For any positive integer x, RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root using units digit:
Let us consider the number 2744.
The unit digit is 4; therefore, the unit digit in the cube root of 2744 will be 4.
After striking out the units, tens, and hundreds digits of the given number, we are left with 2.
Now, 1 is the largest number whose cube is less than or equal to 2.
Therefore, the tens digit of the cube root of 2744 is 1. 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Thus 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =3×14=42 

(iv) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (For any positive integer xRD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root using units digit:
Let us consider the number 15625.
The unit digit is 5; therefore, the unit digit in the cube root of 15625 will be 5.
After striking out the units, tens and hundreds digits of the given number, we are left with 15.
Now, 2 is the largest number whose cube is less than or equal to 15 ((23<15<33)23<15<33.
Therefore, the tens digit of the cube root of 15625 is 2. 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Also 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 9, because 9×9×9=729

Thus 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =9×25=225 

Question 4: Evaluate:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 4:Property:
For any two integers a and b, RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(i) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =4×6=24 

(ii) Use above property and proceed as follows: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×17=34 

(iii) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (∵∵ 700=2×2×5×5×7 and  49=7×7)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=2×5×7=70

(iv) From the above property, we have: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  =125×a2(5×a2) 

 (∵ RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev=a×a=a2 and  RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =5)

=125a25a2=120a2

Question 5: Find the cube root of each of the following rational numbers:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 5: (i) Let us consider the following rational number:

- 125/729

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= - 5/9   ( 729=9×9×9 and 125 = 5×5×5729=9×9×9 and 125 = 5×5×5) 

(ii) Let us consider the following rational number: 

10648/12167

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root by factors:

On factorising 10648 into prime factors, we get:
10648=2×2×2×11×11×1110648=2×2×2×11×11×11
On grouping the factors in triples of equal factors, we get:
10648={2×2×2}×{11×11×11}10648=2×2×2×11×11×11
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×11=22106483=2×11=22

Also
On factorising 12167 into prime factors, we get:
12167=23×23×2312167=23×23×23
On grouping the factors in triples of equal factors, we get:
12167={23×23×23}12167=23×23×23
Now, taking one factor from the triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= 22/23

(iii) Let us consider the following rational number:

-19683/24389

Now, 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root by factors:
On factorising 19683 into prime factors, we get:
19683=3×3×3×3×3×3×3×3×319683=3×3×3×3×3×3×3×3×3

On grouping the factors in triples of equal factors, we get:
19683={3×3×3}×{3×3×3}×{3×3×3}19683=3×3×3×3×3×3×3×3×3
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =3×3×3=27196833=3×3×3=27

Also
On factorising 24389 into prime factors, we get:
24389=29×29×2924389=29×29×29
On grouping the factors in triples of equal factors, we get:
24389={29×29×29}24389=29×29×29
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= -27/ 29

(iv) Let us consider the following rational number: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (686 and 3456 are not perfect cubes; therefore, we simplify it as 686/34566863456 by prime factorisation.) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= -7/ 12

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(v) Let us consider the following rational number:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Cube root by factors: 

On factorising 39304 into prime factors, we get:
39304=2×2×2×17×17×1739304=2×2×2×17×17×17
On grouping the factors in triples of equal factors, we get:
39304={2×2×2}×{17×17×17}39304=2×2×2×17×17×17
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×17=34 

Also
On factorising 42875 into prime factors, we get:
42875=5×5×5×7×7×742875=5×5×5×7×7×7
On grouping the factors in triples of equal factors, we get:
42875={5×5×5}×{7×7×7}42875=5×5×5×7×7×7
Now, taking one factor from each triple, we get: 

 RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =5×7=35 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= 34/35

Question 6: Find the cube root of each of the following rational numbers:
(i) 0.001728
(ii) 0.003375
(iii) 0.001
(iv) 1.331

Answer 6: (i) We have: 

0.001728=1728/1000000 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Now 

On factorising 1728 into prime factors, we get:
1728=2×2×2×2×2×2×3×3×31728=2×2×2×2×2×2×3×3×3
On grouping the factors in triples of equal factors, we get:
1728={2×2×2}×{2×2×2}×{3×3×3} 

Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×2×3=1217283=2×2×3=12

Also 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 100

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  12/100 =  0.12

(ii) We have: 

0.003375= 3375/ 10000000.003375=33751000000
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Now 

On factorising 3375 into prime factors, we get:
3375=3×3×3×5×5×53375=3×3×3×5×5×5
On grouping the factors in triples of equal factors, we get:
3375={3×3×3}×{5×5×5}3375=3×3×3×5×5×5
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =3×5=1533753=3×5=15

Also 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =10010000003=100×100×1003=100

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 15/100 = 0.15

(iii) We have:

 RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 1/10 = 0.1

(iv) We have:  

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 11/10 = 1.1

Question 7: Evaluate each of the following

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 7:

(i) To evaluate the value of the given expression, we need to proceed as follows: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=3+0.2+0.4=3.6 Thus, the answer is 3.6. 

(ii) To evaluate the value of the given expression, we need to proceed as follows: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=10+0.20.5=9.7

Thus, the answer is 9.7. 

(iii) To evaluate the value of the given expression, we need to proceed as follows: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Thus, the answer is 1. 

(iv) To evaluate the value of the expression, we need to proceed as follows: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 1=11=0 

Thus, the answer is 0. 

(v) To evaluate the value of the expression, we need to proceed as follows:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =13/10 =1.3 

Thus, the answer is 1.3. 

Question 8: Show that: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 8:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 9/10

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 9/10

Because LHS is equal to RHS, the equation is true. 

(ii) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = -8/7

RHS = 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

= -8/7

Because LHS is equal to RHS, the equation is true. 

Question 9: Fill in the blanks:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 9:

(i) 5 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 3×5

 RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=5×3 

 =3×5=3×5    (Commutative law) 

(ii) 8×8=648×8=64
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(iii) 3 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 12=4×3

(iv) 20 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(v) 7×8=567×8=56

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(vi) 4×5×6=1204×5×6=120

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(vii) 3 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

(viii) 11 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 9/11

(ix) 13×13×13=2197

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev13×13×13=2197

Question 10: The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.

Answer 10: Volume of a cube is given by: 

V=s3V=s3, where s = side of the cube 

Now
s3=474.552 cubic metres

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRevRD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev To find the cube root of 474552, we need to proceed as follows:

On factorising 474552 into prime factors, we get:
474552=2×2×2×3×3×3×13×13×13474552=2×2×2×3×3×3×13×13×13
On grouping the factors in triples of equal factors, we get:
474552={2×2×2}×{3×3×3}×{13×13×13}474552=2×2×2×3×3×3×13×13×13
Now, taking one factor from each triple, we get: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev =2×3×13=78 

Also 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev = 7.8

Thus, the length of the side is 7.8 m. 

Question 11: Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Answer 11: Let the numbers be 2x, 3x and 4x. 

According to the question: 

(2x)3+(3x)3+(4x)3=0.3341258x3+27x3+64x3=0.3341258x3+27x3+64x3=0.33412599x3=0.334125 RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Thus, the numbers are: 

2×0.15=0.30 3×0.15=0.454×0.15=0.60 Question 12: Find the side of a cube whose volume is RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 12: Volume of a cube with side s is given by: 
V=s3V=s3

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

29/6

Question 13: Evaluate: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

Answer 13:

(i) 36 and 384 are not perfect cubes; therefore, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev for any two integers a and b 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

=2×2×2×3=24

Thus, the answer is 24. 

(ii) 96 and 122 are not perfect cubes; therefore, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRevfor any two integers a and b 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev(By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=2×2×2×3=24 Thus, the answer is 24.

(iii) 100 and 270 are not perfect cubes; therefore, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRevfor any two integers a and b 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

=2×3×5=30 Thus, the answer is 30. 

(iv) 121 and 297 are not perfect cubes; therefore, we use the following property: RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  for any two integers a and b 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=11×3=33 Thus, the answer is 33. 

Question 14: Find The cube roots of the numbers 3048625, 20346417, 210644875, 57066625 using the fact that
(i) 3048625 = 3375 × 729
(ii) 20346417 = 9261 × 2197
(iii) 210644875 = 42875 × 4913
(iv) 57066625 = 166375 × 343

Answer 14: 

(i) To find the cube root, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev for two integers a and b 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By the above property)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev 

=3×5×9=135 Thus, the answer is 135. 

(ii) To find the cube root, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev for two integers a and b 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By the above property) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=3×7×13=273 Thus, the answer is 273. 

(iii) To find the cube root, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev for two integers a and b 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  (By the above property) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=5×7×17=595 Thus, the answer is 595. 

(iv) To find the cube root, we use the following property: 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev for two integers a and b 

Now 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev  (By the above property) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev (By prime factorisation) 

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-4) Class 8 Notes | EduRev

=5×11×7=385 Thus, the answer is 385. 

Question 15: Find the  units digit of the cube root of the following numbers:
(i) 226981
(ii) 13824
(iii) 571787
(iv) 175616

Answer 15: (i) Cube root using units digit:
Let us consider the number 226981.
The unit digit is 1; therefore, the unit digit of the cube root of 226981 is 1.
(ii) Cube root using units digit:
Let us consider the number 13824.
The unit digit is 4; therefore, the unit digit of the cube root of 13824 is 4.
(iii) Cube root using units digit:
Let us consider the number 571787.
The unit digit is 7; therefore, the unit digit of the cube root of 571787 is 3.
(iv) Cube root using units digit:
Let us consider the number 175616.
The unit digit is 6; therefore, the unit digit of the cube root of 175616 is 6. 

Question 16: Find the tens digit of the cube root of each of the numbers in Q. No. 15.

Answer 16: (i) Let us consider the number 226981.
The unit digit is 1; therefore, the unit digit of the cube root of 226981 is 1.
After striking out the units, tens and hundreds digits of the given number, we are left with 226.
Now, 6 is the largest number, whose cube is less than or equal to 226 (63<226<7363<226<73).
Therefore, the tens digit of the cube root of 226981 is 6.
(ii) Let us consider the number 13824.
The unit digit is 4; therefore, the unit digit of the cube root of 13824 is 4.
After striking out the units, tens and hundreds digits of the given number, we are left with 13.
Now, 2 is the largest number, whose cube is less than or equal to 13 (23<13<3323<13<33).
Therefore, the tens digit of the cube root of 13824 is 2.
(iii) Let us consider the number 571787.
The unit digit is 7; therefore, the unit digit of the cube root of 571787 is 3.
After striking out the units, tens and hundreds digits of the given number, we are left with 571.
Now, 8 is the largest number, whose cube is less than or equal to 571 (83<571<9383<571<93).
Therefore, the tens digit of the cube root of 571787 is 8.
(iv) Let us consider the number 175616.
The unit digit is 6; therefore, the unit digit of the cube root of 175616 is 6.
After striking out the units, tens and hundreds digits of the given number, we are left with 175.
Now, 5 is the largest number, whose cube is less than or equal to 175 (53<175<6353<175<63).
Therefore, the tens digit of the cube root of 175616 is 5. 

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