• question_answer If $x=3+2\sqrt{2},$ then find the value of ${{x}^{1/2}}-{{x}^{-1/2}}$. A)  $\frac{1}{2}$ B)  $\sqrt{2}$ C)  2 D)  None of these

Given, $x=3+2\sqrt{2}={{(\sqrt{2}+1)}^{2}}$ $\Rightarrow$ ${{x}^{1/2}}=\sqrt{2}+1$ $\therefore$ ${{x}^{-1/2}}=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1$ Hence, ${{x}^{1/2}}-{{x}^{-1/2}}=\sqrt{2}+1-\sqrt{2}+1=2$