RD Sharma solution class 8 chapter 3 Square and Square roots Exercise 3.7

Exercise 3.7

Page-3.52

Question 1:

Find the square root in decimal form:
84.8241

Answer 1:

Hence, the square root of 84.8241 is 9.21.

Question 2:

Find the square root in decimal form:
0.7225

Answer 2:

Hence, the square root of 0.7225 is 0.85.

Question 3:

Find the square root in decimal form:
0.813604

Answer 3:

Hence, the square root of 0.813604 is 0.902.

Question 4:

Find the square root in decimal form:
0.00002025

Answer 4:

Hence, the square root of 0.00002025 is 0.0045.

Question 5:

Find the square root in decimal form:
150.0625

Answer 5:

Hence, the square root of 150.0625 is 12.25.

Question 6:

Find the square root in decimal form:
225.6004

Answer 6:

Hence, the square root of 225.6004 is 15.02

Question 7:

Find the square root in decimal form:
3600.720036

Answer 7:

Hence, the square root of 3600.720036 is 60.006.

Question 8:

Find the square root in decimal form:
236.144689

Answer 8:

Hence, the square root of 236.144689 is 15.367.

Question 9:

Find the square root in decimal form:
0.00059049

Answer 9:

Hence, the square root of 0.00059049 is 0.0243.

Question 10:

Find the square root in decimal form:
176.252176

Answer 10:

Hence, the square root of 176.252176 is 13.276.

 

Question 11:

Find the square root in decimal form:
9998.0001

Answer 11:

Hence, the square root of 9998.0001 is 99.99.

Question 12:

Find the square root in decimal form:
0.00038809

Answer 12:

Hence, the square root of 0.00038809 is 0.0197.

Question 13:

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

Answer 13:

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.

Question 14:

The area of a square playground is 256.6404 square metres. Find the length of one side of the playground.

Answer 14:

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 metres.

Question 15:

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

Answer 15:

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.

Question 16:

Simplify:
(i) $\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}$
(ii) $\frac{\sqrt{0.2304}+\sqrt{0.1764}}{\sqrt{0.2304}-\sqrt{0.1764}}$

Answer 16:

(i) We have:
$$\begin{gathered} \sqrt{59.29}=\sqrt{\frac{5929}{100}}=\frac{\sqrt{7\times 7\times 11\times 11}}{10}=\frac{7\times 11}{10}=7.7 \\ \sqrt{5.29}=\sqrt{\frac{529}{100}}=\frac{\sqrt{529}}{\sqrt{100}}=\frac{23}{10}=2.3 \\ \frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}=\frac{7.7-2.3}{7.7+2.3}=\frac{5.4}{10}=0.54 \end{gathered}$$


(ii) We have:
$$\begin{gathered} \sqrt{0.2304}=\sqrt{\frac{2304}{10000}} \\ =\frac{\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}}{\sqrt{10000}} \\ =\frac{2\times 2\times 2\times 2\times 3}{100} \\ =0.48 \\ \sqrt{0.1764}=\sqrt{\frac{1764}{10000}} \\ =\frac{\sqrt{2\times 2\times 3\times 3\times 7\times 7}}{\sqrt{10000}} \\ =\frac{2\times 3\times 7}{100} \\ =0.42 \\ \frac{\sqrt{0.2304}+\sqrt{0.1764}}{\sqrt{0.2304}-\sqrt{0.1764}}=\frac{0.48+0.42}{0.48-0.42}=\frac{0.9}{0.06}=15 \end{gathered}$$
                  

Question 17:

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

Answer 17:

We have:
$\sqrt{50625}=\sqrt{3\times 3\times 3\times 3\times 5\times 5\times 5\times 5}=3\times 3\times 5\times 5=225$

Next, we will calculate $\sqrt{506.25} \mathrm{and} \sqrt{5.0625}$

$$\begin{gathered} \sqrt{506.25}=\sqrt{\frac{50625}{100}}=\frac{\sqrt{50625}}{\sqrt{100}}=\frac{225}{10}=22.5 \\ \sqrt{5.0625}=\sqrt{\frac{50625}{10000}}=\frac{\sqrt{50625}}{\sqrt{10000}}=\frac{225}{100}=2.25 \\ \sqrt{506.25}+\sqrt{5.0625}=22.5+2.25=24.75 \end{gathered}$$

Question 18:

Find the value of $\sqrt{103.0225}$ and hence find the value of
(i) $\sqrt{10302.25}$
(ii) $\sqrt{1.030225}$

Answer 18:

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:

$$\begin{gathered} \left(\mathrm{i}\right) \sqrt{10302.25}=\sqrt{103.0225\times 100}=\sqrt{103.0225}\times \sqrt{100}=10.15\times 10=101.5 \\ \left(\mathrm{ii}\right) \sqrt{1.030225}=\sqrt{\frac{103.0225}{100}}=\frac{\sqrt{103.0225}}{\sqrt{100}}=\frac{10.15}{10}=1.015 \end{gathered}$$