Question

If $p=5+2\sqrt{6},$ then $\sqrt{p}$ is equal to

• A. $\sqrt{3}-\sqrt{2}$
• B. $\sqrt{5}+\sqrt{3}$
• C. $\sqrt{3}+\sqrt{2}$
• D. $\sqrt{3}+\sqrt{6}$

Answer 1

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

$p=5+2\sqrt{6}$
$\Rightarrow p=3+2+2\sqrt{6}$
$\Rightarrow p=(\sqrt{3}{)}^2+(\sqrt{2}{)}^2+2\sqrt{3}\sqrt{2}$
$\Rightarrow p=(\sqrt{3}+\sqrt{2}{)}^2$
$\Rightarrow \sqrt{p}=\sqrt{3}+\sqrt{2}$