Question

Find the square root of

$5-2\sqrt{6}$

• A. $\sqrt{13}-\sqrt{2}$
• B. $\sqrt{3}-\sqrt{2}$
• C. $\sqrt{5}-\sqrt{3}$
• D. $\sqrt{5}-\sqrt{2}$

Answer 1

Answer: (B)

$\sqrt{3}-\sqrt{2}$

$5-2\sqrt{6}=3+2-2\sqrt{6}$

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

Using $(a-b{)}^2=a^2+b^2-2ab$

$5-2\sqrt{6}=(\sqrt{3}-\sqrt{2}{)}^2$
$\sqrt{5-2\sqrt{6}}=(\sqrt{3}-\sqrt{2})$

$So,thesquarerootof(5-2\sqrt{6})=\sqrt{3}-\sqrt{2}$