Question

If $x=\sqrt{7+2\sqrt{10}}$, then x = _____

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

Answer 1

The correct option is A

$\sqrt{2}+\sqrt{5}$

$x=\sqrt{7+2\sqrt{10}}$

=$\sqrt{2+5+2\left(\sqrt{2}\right)\left(\sqrt{5}\right)}$

=$\sqrt{(\sqrt{2}{)}^2+(\sqrt{5}{)}^2+2\left(\sqrt{2}\right)\left(\sqrt{5}\right)}$

=$\sqrt{(\sqrt{2}+\sqrt{5}{)}^2}$

=$\sqrt{2}+\sqrt{5}$