Question

The square root of $5+2\sqrt{6}$ is:

• A. $\sqrt{3}+2$
• B. $\sqrt{3}-\sqrt{2}$
• C. $\sqrt{2}-\sqrt{3}$
• D. $\sqrt{3}+\sqrt{2}$

Answer 1

The correct option is D $\sqrt{3}+\sqrt{2}$

$5+2\sqrt{6}$

$=3+2+2\sqrt{6}$

$=3+2\sqrt{6}+2$

$=(\sqrt{3}{)}^2+2\sqrt{3\times 2}+(\sqrt{2}{)}^2=(\sqrt{3}+\sqrt{2}{)}^2$.

$\therefore \sqrt{5+2\sqrt{6}}=\pm \sqrt{(3+\sqrt{2}{)}^2}=\pm (\sqrt{3}+\sqrt{2})$ , which is the required solution.

Therefore, option $D$ is correct.