Question

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

Answer 1

Explanation:

$3+2\sqrt2$

$= 2+2\sqrt2+ 1$

$=(\sqrt2)^2 + 2(\sqrt2)(1)+(\sqrt1)^2$

$=(\sqrt2+1)^2$ [because $a^2 + 2ab + b^2 = (a+b)^2$]

∴ $\sqrt{3+2\sqrt2}$

$=\sqrt{(\sqrt2+1)^2$

$=\sqrt2 + 1$

Answer: √2+1

I hope this helps. :D