If \(x=3+2\sqrt{2}\), then the value of \((\sqrt{x}-\frac{1}{\sqrt{x}})\) is:
Answer: B
\((\sqrt{x}-\frac{1}{\sqrt{x}})^{2}=x+\frac{1}{x}-2\)
\(= (3+2\sqrt{2})+\frac{1}{(3+2\sqrt{2})}-2\)
\(= (3+2\sqrt{2})+\frac{1}{(3+2\sqrt{2})}\times\frac{(3-2\sqrt{2})}{(3-2\sqrt{2})}-2\)
\(= (3+2\sqrt{2})+(3+2\sqrt{2})-2\)
= 4
\(\therefore (\sqrt{x}-\frac{1}{\sqrt{x}})=2\)