Question

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

Answer 1

$\sqrt{3}=1.732,\sqrt{5}=2.236$

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

(Rationalising the denominator)

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

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

$=3[2.236+1.732]=3\left(3.968\right)$

$=11.904$