Question

Simplify $\sqrt{3+2\sqrt{2}}$.

Answer 1

Given, $\sqrt{3+2\sqrt{2}}$

$=\sqrt{3+2\sqrt{2}\times \sqrt{1}}(\sqrt{2}\text{can be written as}\sqrt{2}\times \sqrt{1})$

$=\sqrt{2+1+2\sqrt{2}\times \sqrt{1}}$

$=\sqrt{(\sqrt{2}{)}^2+(\sqrt{1}{)}^2+2\sqrt{2}\times \sqrt{1}}$

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

$=\sqrt{(\sqrt{2}+\sqrt{1}{)}^2}$

$=\sqrt{2}+\sqrt{1}$

$=\sqrt{2}+1$