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}} $

Given: 

\( \frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}} \)

To do: 

We have to simplify \( \frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}} \).

Solution:

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

Square root of 59.29 is,

Square root of 5.29 is,

Therefore,

$\frac{\sqrt{59.29}-\sqrt{5.29}}{\sqrt{59.29}+\sqrt{5.29}}=\frac{7.7-2.3}{7.7+2.3}$

$=\frac{5.4}{10}$

$=0.54$

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

Square root of 0.2304 is,

Square root of 0.1764 is,

Therefore,

$\frac{\sqrt{0.2304}+\sqrt{0.1764}}{\sqrt{0.2304}-\sqrt{0.1764}}=\frac{0.48+0.42}{0.48-0.42}$

$=\frac{0.90}{0.06}$

$=\frac{90}{6}$

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Updated on: 10-Oct-2022

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