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NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Exercise 7.1 

Question 1: Which of the following numbers are not perfect cubes: 

(i) 216 

(ii) 128 

(iii) 1000 

(iv) 100 

(v) 46656 

Answer : 

(i) 216

Prime factors of 216 = 2x2x2x3x3x3

Here all factors are in groups of 3’s [in triplets) Therefore, 216 is a perfect cube number.

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

(ii)

Prime factors of 128 =2x2x2x2x2x2x2

Here one factor 2 does not appear in a 3's group.

Therefore, 128 is not a perfect cube.

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

(iii)

Prime factors of 1000 =2x2x2x3x3x3

Here all factors appear in 3's group.

Therefore, 1000 is a perfect cube.

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

(iv)

Prime factors of 100 =2x2x5x5

Here all factors do not appear in 3’s group.

Therefore, 100 is not a perfect cube.

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

(v)

Prime factors of 46656 = 2x2x2 x2x2x2x3x3x3x3x3x3

Here all factors appear in 3's group.

Therefore, 46656 is a perfect cube.

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Question 2: 

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube: 

(i) 243 

(ii) 256 

(iii) 72 

(iv) 675 

(v) 100 

Answer 2: 

(i)  

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 243 =3x3x3x3x3

Here 3 does not appear in 3's group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube.

(ii)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 256 = 2 x 2 x 2 x 2x2x 2x2x2

Here one factor 2 is required to make a 3's group.

Therefore, 256 must be multipl ied by 2 to make it a perfect cube.

(iii)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 72 = 2x2x2x3x3

Here 3 does not appear in 3's group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube.

(iv)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 675 =3x3x3x5x5

Here factor 5 does not appear in 3's group.

Therefore 675 must be multiplied by 3 to make it a perfect cube.

(v)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of l00 = 2x2x5x5

Here factor 2 and 5 both do not appear in 3's group.

Therefore 100 must be multiplied by 2 x 5 = 10 to make it a perfect cube

Question 3: 

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 

(i) 81 

(ii) 128 

(iii) 135 

(iv) 192 

(v) 704 

Answer 3:

(i)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 81 = 3x3x3x3

Here one factor 3 is not grouped in triplets.

Therefore 81 must be divided by 3 to make it a perfect cube.

(ii)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 128 =2x2x2x2x2x2x2

Here one factor 2 does not appear in a 3's group.

Therefore, 128 must be divided by 2 to make it a perfect cube

(iii)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 135 = 3x3x3x5

Here one factor 5 does not appear in a triplet.

Therefore, 135 must be divided by 5 to make it a perfect cube.

(iv)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 192 =2x2x2x2x2x2x3

Here one factor 3 does not appear in a triplet

Therefore, 192 must be divided by 3 to make it a perfect cube.

(v)

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Prime factors of 704 = 2x2x2x2x2x2x11

Here one factor 11 does not appear in a triplet

Therefore, 704 must be divided by 11 to make it a perfect cube.

Question 4: 

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube? 

Answer 4: 

Given numbers = 5 x 2 x 5

Since, Factors of 5 and 2 both are not in group of three.

Therefore, the number must be multiplied by 2 x 2 x 5 = 20 to make it a perfect cube.

Hence he needs 20 cuboids.

Exercise 7.2 

Question 1: Find the cube root of each of the following numbers by prime factorization method: 

(i) 64

(ii) 512

(iii) 10648

(iv] 27000

(v) 15625

[vi] 13824

(vii) 110592

[viii] 46656

(ix) 175616

(x) 91125

Answer 1: 

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

 

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

Question 2: 

State true or false: 

(i) Cube of any odd number is even.
 (ii) A perfect cube does not end with two zeroes.
 (iii) If square of a number ends with 5, then its cube ends with 25.
 (iv) There is no perfect cube which ends with 8.
 (v) The cube of a two digit number may be a three digit number.
 (vi) The cube of a two digit number may have seven or more digits.
 (vii) The cube of a single digit number may be a single digit number.

Answer : 

(i) False

Since, 1'=1,3= 27,53 = 125,. ......... are all odd.

(ii) True

Since, a perfect cube ends with three zeroes.

e.g. 103 = 1000,203 =8000,303 = 27000,...... soon

(iii) False

Since, 52 = 25,53 = 125, 152 = 225,153 = 3375 [Did not end with 2 5)

(iv) False

Since 12=1728 [Ends with 8]

And 22=10648 [Ends with 8]

(v) False

Since 10=1000 [Four digit number]

And 113 =1331 [Four digit number]

[vi] False

Since 993 = 970299 [Six digit number]

(vii) True

13 =1 [Single digit number]

23 =8 [Single digit number]

Question 3: 

You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768. 

Answer : 

We know that 103 = 1000 and Possible cube of 113 = 1331
Since, cube of unit's digit I3 = 1
Therefore, cube root of 1331 is 11,

4913

We know that 73 = 343
Next number comes with 7 as unit place 173 =4913
Hence, cube root of 4913 is 17.

12167

We know that 33 = 27
Here in cube, ones digit is 7
Now next number with 3 as ones digit 133 = 2197
And next number with 3 as ones digit 233 =12167 Hence cube root of 12167 is 23.

32768

We know that 23 = 8
Here in cube, ones digit is 8
Now next number with 2 as ones digit I23 = 1728
And next number with 2 as ones digit 223 = 10648
And next number with 2 as ones digit 323 = 32768
Hence cube root of 32768 is 32.

 

The document NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots is a part of Class 8 category.
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FAQs on NCERT Solutions for Class 8 Maths - Cubes and Cubes Roots

1. What is the definition of a cube?
Ans. A cube is a three-dimensional solid object bounded by six square faces, angles of which meet at 90 degrees. It has a regular structure with all its sides having equal length.
2. What is the formula to calculate the volume of a cube?
Ans. The formula to calculate the volume of a cube is V = s^3, where V is the volume and s is the length of one side of the cube.
3. What is the cube root of 27?
Ans. The cube root of 27 is 3. This is because 3 multiplied by 3 multiplied by 3 is equal to 27.
4. What is the relationship between the cube and the cube root?
Ans. The cube root of a number is the number that when multiplied by itself three times gives the original number. Similarly, the cube of a number is obtained by multiplying the number by itself three times. Therefore, the cube and the cube root are inverse operations of each other.
5. What are some real-world applications of cubes and cube roots?
Ans. Cubes and cube roots have numerous real-world applications in fields such as architecture, engineering, and mathematics. For example, architects use cubes to design buildings, while engineers use cubes to design machinery. Additionally, cube roots are used in medicine to determine the dosage of drugs and in finance to calculate compound interest.
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