Question

ROOT(6+2*ROOT3+2*ROOT2+2*ROOT6)

Answer 1

You have, $\sqrt{6+2\sqrt{3}+2\sqrt{2}+2\sqrt{6}}$
= $\sqrt{(\sqrt{3})^{2}+(\sqrt{2})^{2}+(\sqrt{1}^{2})+2(\sqrt{3}+\sqrt{2}+\sqrt{6})}$
From the identity, a²+b²+c²+2(ab+bc+ca) = (a+b+c)², given number is, = $\sqrt{( \sqrt{3}+\sqrt{2}+1)^{2}} = \sqrt{3} + \sqrt{2} +1$.