If $x=3+2 sqrt{2}$, then the value of $left(sqrt{x}-frac{1}{sqrt{x}} ight)$ is :

$x=3+2 sqrt{2}$

$herefore frac{1}{x}=frac{1}{3+2 sqrt{2}}$

$=frac{1}{3+2 sqrt{2}} imes frac{3-2 sqrt{2}}{3-2 sqrt{2}}$

$=frac{3-2 sqrt{2}}{9-8}=3-2 sqrt{2}$

$hereforeleft(sqrt{x}-frac{1}{sqrt{x}} ight)^{2}=x+frac{1}{x}-2$

$=3+2 sqrt{2}+3-2 sqrt{2}-2=4$

$herefore sqrt{x}-frac{1}{sqrt{x}}=2$