Given that $\sqrt2, = 1.414, \sqrt3 = 1.732, \sqrt5 = 2.236$ and $\sqrt7 = 2.646$. Evaluate each of the following:
(i) $ \sqrt{\frac{144}{7}} $
(ii) $ \sqrt{\frac{2500}{3}}

To do: 

We have to find the values of 

(i) \( \sqrt{\frac{144}{7}} \)

(ii)  \( \sqrt{\frac{2500}{3}} \)

Solution:

(i) $\sqrt{\frac{144}{7}}=\frac{\sqrt{144}}{\sqrt7}$

$=\frac{\sqrt{144} \times \sqrt{7}}{\sqrt{7} \times \sqrt{7}}$

$=\frac{12 \sqrt{7}}{7}$

$=\frac{12 \times 2.646}{7}$

$=\frac{31.752}{7}$

$=4.536$

(ii) $\sqrt{\frac{2500}{3}}=\frac{\sqrt{2500}}{\sqrt{3}}$

$=\frac{\sqrt{2500} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$=\frac{50 \times \sqrt{3}}{3}$

$=\frac{50 \times 1.732}{3}$

$=\frac{86.6}{3}$

$=28.8666$

$=28.867$

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Updated on: 10-Oct-2022

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