Question

$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

Answer 1

Given: $\frac{1}{\sqrt{9}-\sqrt{8}}$
$=\frac{1}{\sqrt{3\times 3}-\sqrt{2\times 2\times 2}}$
$=\frac{1}{\sqrt{3^2}-\sqrt{2^2\times 2}}$
$=\frac{1}{3-2\sqrt{2}}$
Rationalizing the denominator
$=\frac{3+2\sqrt{2}}{(3-2\sqrt{2})(3+2\sqrt{2})}$
$=\frac{3+2\sqrt{2}}{(3{)}^2-(2\sqrt{2}{)}^2}$
$=\frac{3+2\sqrt{2}}{9-8}$
$=\frac{3+2\sqrt{2}}{1}$
$=3+2\sqrt{2}$
$\therefore \left(a\right)$ is the Correct Option