Simplify: 3+2 2. - Vidyadip

Question

Simplify: $\sqrt{3+2\sqrt2}.$

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Answer

We are asked to simplify $\sqrt{3+2\sqrt2}.$ It can be written in the form $(\text{a}+\text{b})^2=\text{a}^2+\text{b}^2+2\text{ab}$ as $\sqrt{3+2\sqrt2}=\sqrt{2+1+2\times1\times\sqrt2}$
$=\sqrt{\big(\sqrt2\big)^2+(1)^2+2\times1\times\sqrt2}$
$=\sqrt{\big(\sqrt2+1\big)^2}$
$=\sqrt2+1$ Hence the value of given expression is $\sqrt2+1.$

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