RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Class 8: RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The document RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 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 2: Find the square root of 12.0068 correct to four decimal places.

Answer 2:

 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

We can round it off to four decimal places, i.e. 3.4651. 

Question 3: Find the square root of 11 correct to five decimal places.

Answer 3: Using the long division method: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 3.31662

Question 4: Given that:RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

 and   RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 evaluate each of the following:

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer 4: Given: √7 = 2.646 

(i) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Given: √3 = 1.732

(ii) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 28.867(ii) 25003=25003=501.732=28.867 

Question 5: Given that: RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 find the square roots of the following: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Answer 5: From the given values, we can simplify the expressions in the following manner: 

(i) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(ii) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iii) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(iv) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

(v) RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Question 6: Using square root table, find the square root
7

Answer 6: From the table, we directly find that the square root of 7 is 2.646. 

Question 7: Using square root table, find the square root
15

Answer 7: Using the table to find √3 and √5

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.732×2.236=3.873

Question 8:Using square root table, find the square root 74

Answer 8: Using the table to find 
RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.414×6.083 

=8.602 

Question 9: Using square root table, find the square root 82 

Answer 9: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 

 =1.414×6.403 

=9.055 

Question 10: Using square root table, find the square root 198

Answer 10: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.414×3×3.317 

= 14.070 

Question 11: Using square root table, find the square root

540

Answer 11: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=2×3×1.732×2.2361 

=23.24 

Question 12: Using square root table, find the square root 8700

Answer 12: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.7321×5.385×10 

=93.27 

Question 13: Using square root table, find the square root 3509

Answer 13: Using the table to find29

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=11×5.3851 

=59.235 

Question 14: Using square root table, find the square root 6929

Answer 14: Using the table to find √14

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=13 ×6.4031 

=83.239 

Question 15: Using square root table, find the square root 25725

Answer 15: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.732 ×5×7×2.646 

=160.41 

Question 16: Using square root table, find the square root 1312

Answer 16: Using the table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=2×2×1.414×6.4031 

=36.222 

Question 17: Using square root table, find the square root 4192

Answer 17: RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The square root of 131 is not listed in the table. Hence, we have to apply long division to find it. 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Substituting the values: 

=   2×2×11.44552×2×11.4455     (using the table to find2)

= 64.75 

Question 18: Using square root table, find the square root 4955

Answer 18: On prime factorisation:
4955 is equal to 5 ×× 991, which means that RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The square root of 991 is not listed in the table; it lists the square roots of all the numbers below 100.
Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Now, we have to find the square root of 49.55. 

We have:  RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Their difference is 0.071.
Thus, for the difference of 1 (50 - 49), the difference in the values of the square roots is 0.071.
For the difference of 0.55, the difference in the values of the square roots is:
0.55 ×× 0.0701 = 0.03905 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 7+0.03905=7.03905 

Finally, we have: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 ×10=7.03905×10=70.3905

Question 19: Using square root table, find the square root 99/144

Answer 19:

 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8    (using the square root table to find √11)

  =0.829  

Question 20: Using square root table, find the square root 57/169

Answer 20:

 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8  (using the square root table to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

 0.581

Question 21: Using square root table, find the square root 101/169

Answer 21: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

The square root of 101 is not listed in the table. This is because the table lists the square roots of all the numbers below 100.
Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Now, we have to find the square root of 1.01. 

We have: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Their difference is 0.414.
Thus, for the difference of 1 (2 - 1), the difference in the values of the square roots is 0.414.
For the difference of 0.01, the difference in the values of the square roots is:
0.01 ×× 0.414 = 0.00414 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 1+0.00414=1.00414

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 ×10=1.00414×10=10.0414 
Finally, RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 
This value is really close to the one from the key answer. 

Question 22: Using square root table, find the square root
13.21

Answer 22: From the square root table, we have: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Their difference is 0.136.
Thus, for the difference of 1 (14 - 13), the difference in the values of the square roots is 0.136.
For the difference of 0.21, the difference in the values of their square roots is:
0.136×0.21=0.028560.136×0.21=0.02856

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 3.606+0.02856≈3.635

Question 23: Using square root table, find the square root

Answer 23: We have to find RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

From the square root table, we have: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Their difference is 0.107.
Thus, for the difference of 1 (22 - 21), the difference in the values of the square roots is 0.107.
For the difference of 0.97, the difference in the values of their square roots is:
0.107×0.97=0.1040.107×0.97=0.104
RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 4.583+0.104≈4.687

Question 24: Using square root table, find the square root 110

Answer 24:

 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.414×2.236×3.317        (Using the square root table to find all the square roots) 

=10.488 

Question 25: Using square root table, find the square root

1110 

Answer 25: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=1.414×1.732×2.236×6.083       (Using the table to find all the square roots )=33.312

Question 26: Using square root table, find the square root

11.11

Answer 26: We have: 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

Their difference is 0.1474.
Thus, for the difference of 1 (12 - 11), the difference in the values of the square roots is 0.1474.
For the difference of 0.11, the difference in the values of the square roots is:
0.11 ×× 0.1474 = 0.0162 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 3.3166+0.0162=3.328≈3.333

Question 27: The area of a square field is 325 m2. Find the approximate length of one side of the field.

Answer 27: The length of one side of the square field will be the square root of 325.
 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=5×3.605 

=18.030  

Hence, the length of one side of the field is 18.030 m. 

Question 28: Find the length of a side of a sqiare, whose area is equal to the area of a rectangle with sides 240 m and 70 m.

Answer 28: The area of the rectangle = 240 m ×× 70 m = 16800 m2
Given that the area of the square is equal to the area of the rectangle.
Hence, the area of the square will also be 16800 m2.
The length of one side of a square is the square root of its area. 

 

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

=2×2×5 RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8

RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 =129.60 m 

Hence, the length of one side of the square is 129.60 m

The document RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-7) Notes | Study RD Sharma Solutions for Class 8 Mathematics - Class 8 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

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