​ Simplify √3+2√ 2

Question

Simplify \(\sqrt{3+2\sqrt2}\)

Answer 1

Consider, \(\sqrt{3+2\sqrt2}\)

\(\sqrt{3+2\sqrt2}\) = \(\sqrt{(2+1+2\sqrt2)}\)

= \(\sqrt{((\sqrt2)^2+(1)^2+2\times 1\times \sqrt2}\)

As we know,(a+b)² = a² + b² + 2ab

= \(\sqrt{(\sqrt2+1)^2}\)

 = \({\sqrt2+1}\)