# RD Sharma Solutions Class 8 Squares And Square Roots Exercise 3.7

## RD Sharma Solutions Class 8 Chapter 3 Exercise 3.7

### Exercise 3.7

Find the square root of the following numbers in the decimal form:

1.) 84.8241

Square root of 84.821 is 9.21.

2.) 0.7225

Square root of 0.7225 is 0.85.

3.) 0.813604

Square root of 0813604 is 0.902

4.) 0.00002025

Square root of 0.00002025 is 0.0045.

5.) 150.0625

Square root of 150.0625 is 12.25

6.) 225.6004

Square root of 225.6004 is 15.02

7.) 3600.720036

Square root of 3600.720036 is 60.006

8.) 236.144689

Square root of 236.144869 is 15.367 .

9.) 0.00059049

Square of 0.0059049 is 0.0243

10.) 176.252176

Square root of 176.252176 is 13.276

11.) 9998.0001

Square root of 9998.0001 is 99.99.

12.) 0.00038809

Square root of 0.00038809 is 0.0197.

13.) What is that fraction which when multiplied by itself gives 227.798649?

Find the square root:

Required number is 15.093.

14.) The area of a square playground is 256.6404 square meters. Find the length of one side of the playground.

Given: area of a square playground is 256.6404 square meters

To Find: Length of one side of the playground.

The length of one side of the playground is the square root of its area.

So, the length is 16.02 meters.

15.) What is the fraction which when multiplied by itself gives 0.00053361?

Square root of the given number:

0.0231 is the required fraction.

16.) Simplify:

(i) $\frac{\sqrt{59.29} – \sqrt{5.29}}{\sqrt{59.29} + \sqrt{5.29}}$

(ii) $\frac{\sqrt{0.2304} + \sqrt{0.1764}}{\sqrt{0.2304} – \sqrt{0.1764}}$

(i)

$\sqrt{59.29} = \sqrt{\frac{5929}{100}} = \frac{\sqrt{7\times 7\times 11\times 11}}{10} = \frac{7\times 11}{10} = 7.7$

$\sqrt{5.29} = \sqrt{\frac{592}{100}} = \frac{\sqrt{529}}{\sqrt{100}} = \frac{23}{10} = 2.3$

$\frac{\sqrt{59.29} -\sqrt{ 5.29}}{\sqrt{59.29} + \sqrt{5.29}} = \frac{7.7 – 2.3 }{7.7 + 2.3} = \frac{5.4}{10} = 0 .54$

(ii)

$\sqrt{0.2304} = \sqrt{\frac{2304}{10000}}$

= $\frac{\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}}{\sqrt{10000}}$

= $\frac{2\times 2\times 2\times 2\times 3}{100}$ = 0.42

$\frac{\sqrt{0.2304 }+\sqrt{0.1764}}{\sqrt{0.2304} – \sqrt{0.1764}} = \frac{0.48 + 0.42 }{0.48 – 0.42 } = \frac{0.9}{0.06}$ = 15

17.) Evaluate $\sqrt{50625}$ and hence find the value of $\sqrt{506.25} +\sqrt{ 5.0625 }$

$\sqrt{50625} = \sqrt{3\times 3\times 3\times 3\times 5\times 5\times 5\times 5\times 5} = 3\times 3\times \times 5\times 5$ = 225

Now, calculate $\sqrt{506.25}$ and $\sqrt{5.0625}$

$\sqrt{506.25} =\sqrt{ \frac{50625}{100}}= \frac{\sqrt{52625}}{\sqrt{100}} = \frac{225}{10} = 22.5$

$\sqrt{5.0625} =\sqrt{ \frac{50625}{10000}}= \frac{\sqrt{52625}}{\sqrt{10000}} = \frac{225}{100} = 2.25$

$\sqrt{506.25} + \sqrt{5.0625} = 22. 5 + 2.25 = 24.75$

18.) Find the value of $\sqrt{103.0225}$ and hence find the value of:

(i) $\sqrt{10302.25}$

(ii) $\sqrt{1.030225}$

(i) $\sqrt{10302.25} = \sqrt{103.0225\times 100} = \sqrt{103.0225}\times \sqrt{100} = 10.15 \times 10 = 101.5$.
(ii) $\sqrt{1.030225 }= \sqrt{\frac{103.0225}{100}} = \frac{\sqrt{103.0225}}{\sqrt{100}} = \frac{10.15}{10} = 1.015$