Question

Simplify the following.

$3\sqrt{2}+\sqrt[4]{464}+\sqrt[4]{4500}+\sqrt[6]{68}$

Answer 1

$3\sqrt{2}+\sqrt[4]{464}+\sqrt[4]{42500}+\sqrt[6]{68}$
$=3\sqrt{2}+\sqrt[4]{416\times 4}+\sqrt[4]{4625\times 4}+\sqrt[6]{62^3}$
$=3\sqrt{2}+\sqrt[4]{416}\sqrt[4]{44}+\sqrt[4]{4625}\sqrt[4]{44}+\sqrt[6]{62^3}$
$=3\sqrt{2}+\sqrt[4]{42^4}\sqrt[4]{42^2}+\sqrt[4]{45^4}\sqrt[4]{42^4}+\sqrt[6]{62^3}$
$=3\sqrt{2}+2\sqrt{2}+5.\sqrt{2}+\sqrt{2}$
$=(3+2+5+1)\sqrt{2}$
$=11\sqrt{2}$