Question

If $x=3+2\sqrt{2}$ then find the value of $(\sqrt{x}-\frac{1}{\sqrt{x}})$

Answer 1

Given, $x=3+2\sqrt{2}$

Therefore, the value of $(\sqrt{x}-\frac{1}{\sqrt{x}})$ is

$=(\sqrt{3+2\sqrt{2}}-\frac{1}{\sqrt{3+2\sqrt{2}}})$

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

$=\frac{4.828}{2.414}$

$=2$