Question

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

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

Answer 1

Answer: (B)

$\pm 2$

$x=3+2\sqrt{2}$ $\frac{1}{x}=\frac{1}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}}$

$=3-2\sqrt{2}$

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

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

So, $\sqrt{x}-\frac{1}{\sqrt{x}}=\sqrt{4}=\pm 2$ Ans