Find the value of

Question:

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

Solution:

Given,

$\frac{6}{\sqrt{5}-\sqrt{3}}$

Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor

$\sqrt{5}+\sqrt{3}$ for $\frac{1}{\sqrt{5}-\sqrt{3}}$

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

Since, $(a+b)(a-b)=\left(a^{2}-b^{2}\right)$

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

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

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

$=3(2.236+1.732)=3(3.968)=11.904$

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