RD Sharma solution class 8 chapter 3 Square and Square roots Exercise 3.8

Exercise 3.8

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Question 1:

Find the square root of each of the following correct to three places of decimal.
(i) 5
(ii) 7
(iii) 17
(iv) 20
(v) 66
(vi) 427
(vii) 1.7
(viii) 23.1
(ix) 2.5
(x) 237.615
(xi) 15.3215
(xii) 0.9
(xiii) 0.1
(xiv) 0.016
(xv) 0.00064
(xvi) 0.019
(xvii) $\frac{7}{8}$
(xviii) $\frac{5}{12}$
(xix) $2\frac{1}{2}$
(xx) $287\frac{5}{8}$

Answer 1:

(i) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 5 up to three decimal places is 2.236.

(ii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 7 up to three decimal places is 2.646.

(iii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 17 up to three decimal places is 4.123.

(iv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 20 up to three decimal places is 4.472.

(v) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 66 up to three decimal places is 8.124.

(vi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 427 up to three decimal places is 20.664.

(vii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 1.7 up to three decimal places is 1.304.

(viii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 23.1 up to three decimal places is 4.806.

(ix) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 2.5 up to three decimal places is 1.581.

(x) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 237.615 up to three decimal places is 15.415.

(xi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 15.3215 up to three decimal places is 3.914.

(xii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.9 up to three decimal places is 0.949.

(xiii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.1 up to three decimal places is 0.316.

(xiv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.016 up to three decimal places is 0.126.

(xv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.00064 up to three decimal places is 0.025.

(xvi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.019 up to three decimal places is 0.138.

(xvii) We can find the square root up to four decimal places by expanding 7/8 to decimal form up to eight digits to the right of the decimal point as shown below:
$\frac{7}{8}=0.875$
Hence, we have:

So, the square root of 7/8 up to three decimal places is 0.935.

(xviii) We can find the square root up to four decimal places by expanding 5/12 to decimal form up to eight digits to the right of the decimal point as shown below:
$\frac{5}{2}=0.41666666$
Hence, we have:

So, the square root of 5/12 up to three decimal places is 0.645.

(xix) We can find the square root up to four decimal places by expanding  $2\frac{1}{2}$ into decimal form up to eight digits to the right of the decimal point as shown below:
$2\frac{1}{2}=2.50000000$
But, this is the same with the value 2.5 in problem (ix). Hence, the square root of   $2\frac{1}{2}$ is 1.581.

(xx) We can find the square root up to four decimal places by expanding $287\frac{5}{8}$ into decimal form up to eight digits to the right of the decimal point as shown below:
$287\frac{5}{8}=287.62500000$
Hence, we have:

So, the square root of  $287\frac{5}{8}$ up to three decimal places is 16.960.

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Question 2:

Find the square root of 12.0068 correct to four decimal places.

Answer 2:

$\therefore$ $\sqrt{12.0068}=3.46508$ 
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:

$\therefore$ $\sqrt{11}=3.31662$

Question 4:

Given that: $\sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236 \mathrm{and} \sqrt{7}=2.646,$ evaluate each of the following:

(i) $\sqrt{\frac{144}{7}}$
(ii) $\sqrt{\frac{2500}{3}}$

Answer 4:

Given:  $\sqrt{7} = 2.646$
$\left(i\right) \sqrt{\frac{144}{7}}=\frac{\sqrt{144}}{\sqrt{7}}=\frac{12}{2.646}=4.536$

Given: $\sqrt{3} = 1.732$
$\left(\mathrm{ii}\right) \sqrt{\frac{2500}{3}}=\frac{\sqrt{2500}}{\sqrt{3}}=\frac{50}{1.732}=28.867$

Question 5:

Given that: $\sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236 \mathrm{and} \sqrt{7}=2.646,$ find the square roots of the following:
(i) $\frac{196}{75}$
(ii) $\frac{400}{63}$
(iii) $\frac{150}{7}$
(iv) $\frac{256}{5}$
(v) $\frac{25}{50}$

Answer 5:

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

$$\begin{gathered} \left(\mathrm{i}\right) \sqrt{\frac{196}{75}}=\frac{14}{5\sqrt{3}}=\frac{14}{5\times 1.732}=1.617 \\ \left(\mathrm{ii}\right) \sqrt{\frac{400}{63}}=\frac{20}{3\sqrt{7}}=\frac{20}{3\times 2.646}=2.520 \\ \left(\mathrm{iii}\right) \sqrt{\frac{150}{7}}=\frac{5\sqrt{2}\times \sqrt{3}}{\sqrt{7}}=\frac{5\times 1.414\times 1.732}{2.646}=4.628 \\ \left(\mathrm{iv}\right) \sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155 \\ \left(\mathrm{v}\right) \sqrt{\frac{27}{50}}=\frac{3\sqrt{3}}{5\sqrt{2}}=\frac{3\times 1.732}{5\times 1.414}=0.735 \end{gathered}$$