Question

please answer this .

Answer 1

Given to evaluate:-

$\sqrt{22 + 4 \sqrt{10} }$

Solution:-

First of all, we have to know the identity to be used while solving this question.

Identity to be used here:-

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Calculation:-

$\sqrt{22 + 4 \sqrt{10} }$

Can be written like this:-

$\sqrt{2 + 20 + 4 \sqrt{10} }$

$= \sqrt{( \sqrt{2} )^{2} + ( \sqrt{20} )^{2} +2 \times \sqrt{2} \times \sqrt{20} }$

$= \sqrt{ (\sqrt{2} + \sqrt{20})^{2} }$

$= \pm (\sqrt{2} + \sqrt{20} )$

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

Answer:-

$\pm( \sqrt{2} + 2 \sqrt{5} )$