Question

If $x=3-2\sqrt{2}$ then the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$ is

• A. $\sqrt{2}$
• B. $-\sqrt{2}$
• C. 1
• D. $-2$

Answer 1

Answer: (D)

We have,
$x=3-2\sqrt{2}$
$x={\left(\sqrt{2}-1\right)}^2$
$\sqrt{x}=\sqrt{2}-1$
$\frac{1}{\sqrt{x}}=\frac{1}{\sqrt{2}-1}=\sqrt{2}+1$
$\therefore \sqrt{x}-\frac{1}{\sqrt{x}}$
$=\left(\sqrt{2}-1\right)-\left(\sqrt{2}+1\right)=-2$