Question

Find the square root of $7-2\sqrt{10}$

• A. $\sqrt{15}-\sqrt{2}$
• B. $\sqrt{3}-\sqrt{2}$
• C. $\sqrt{5}-\sqrt{3}$
• D. $\sqrt{5}-\sqrt{2}$

Answer 1

The correct option is D $\sqrt{5}-\sqrt{2}$

$7-2\sqrt{10}=5+2-2\sqrt{10}$

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

$7-2\sqrt{10}=(\sqrt{5}-\sqrt{2}{)}^2$

$\sqrt{7-2\sqrt{10}}=\sqrt{5}-\sqrt{2}$