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

## RD Sharma Solutions Class 8 Chapter 3 Exercise 3.7

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

1.) 84.8241

Hence, the square root of 84.821 is 9.21.

2.) 0.7225

Hence, the square root of 0.7225 is 0.85.

3.) 0.813604

Hence, the square root of 0813604 is 0.902

4.) 0.00002025

Hence, the square root of 0.00002025 is 0.0045.

5.) 150.0625

Hence, the square root of 150.0625 is 12.25

6.) 225.6004

Hence, the square root of 225.6004 is 15.02

7.) 3600.720036

Hence, the square root of 3600.720036 is 60.006

8.) 236.144689

Hence, the square root of 236.144869 is 15.367 .

9.).00059049

Hence, the square of 0.0059049 is 0.0243

10.) 176.252176

Hence, the square root of 176.252176 is 13.276

11.) 9998.0001

Hence, the square root of 9998.0001 is 99.99.

12.) 0.00038809

Hence, the square root of 0.00038809 is 0.0197.

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

We have to find the square root of the given number:

Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093.

14.) The area of a square playground is 256.6404 square meters. Find the 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 of one side of the playground is 16.02 meters.

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

We have to find the square root of the given number:

Hence, the fraction, which when multiplied by itself, gives 0.00053361 is 0.0231.

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) We have:

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

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

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

(ii) We have:

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

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

= $\frac{2\times 2\times 2\times 2\times 3}{100}$ = 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 $\sqrt{506.25} +\sqrt{ 5.0625 }$

We have:

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

Next, we 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) $\sqrt{1.030225}$

The value of 103.0225 is:

Hence, the square root of 103.0225 is 10.15

Now, we can solve the following questions as shown below:

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

(ii) $\sqrt{1.030225 }= \sqrt{\frac{103.0225}{100}} = \frac{\sqrt{103.0225}}{\sqrt{100}} = \frac{10.15}{10} = 1.015$

#### Practise This Question

If there are 45 birds out of 150 in a zoo which are migratory. 35 of the total birds are of  Indian origin. Which kind of birds are more in number in the zoo?