Find the value of $ \frac{6}{\sqrt{5}-\sqrt{3}} $, it being given that $ \sqrt{3}=1.732 $ and $ \sqrt{5}=2.236 $.

Given:

\( \sqrt{3}=1.732 \) and \( \sqrt{5}=2.236 \).

To do: 

We have to find the value of \( \frac{6}{\sqrt{5}-\sqrt{3}} \).

Solution:

We know that,

Rationalising factor of a fraction with denominator ${\sqrt{a}}$ is ${\sqrt{a}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}-\sqrt{b}}$ is ${\sqrt{a}+\sqrt{b}}$.

Rationalising factor of a fraction with denominator ${\sqrt{a}+\sqrt{b}}$ is ${\sqrt{a}-\sqrt{b}}$.

Therefore,

$\frac{6}{\sqrt{5}-\sqrt{3}}=\frac{6(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$

$=\frac{6(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^{2}-(\sqrt{3})^{2}}$

$=\frac{6(\sqrt{5}+\sqrt{3})}{5-3}$

$=\frac{6(\sqrt{5}+\sqrt{3})}{2}$

$=3(\sqrt{5}+\sqrt{3})$

$=3[2.236+1.732]$

$=3(3.968)$

$=11.904$

The value of \( \frac{6}{\sqrt{5}-\sqrt{3}} \) is $11.904$.

Tutorialspoint

Updated on: 10-Oct-2022

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