Answer
$9\sqrt[4] {2}$
Work Step by Step
Before we can add these two numbers, we must transform them so that the radicals are similar. Only then can we perform the operation we are asked to do.
Let us expand the radicands in both radicals.
For the first radical, the number $162$ can be rewritten as $(81)(2)$, so:
$\sqrt[4] {(81)(2)}=\sqrt[4]{3^4(2)}=3\sqrt[4]{2}$
For the second radical, $32=16(2)$ so:
$3\sqrt[4] {32}=3\sqrt[4]{16(2)}=3\sqrt[4]{2^4(2)}=3\cdot2\sqrt[4]{2}=6\sqrt[4]{2}$
Finally, we can perform the operation in the original problem because we now have similar radicals and indices for the two terms:
$=3\sqrt[4] {2} + 6\sqrt[4] {2}$
$=(3+6)\sqrt[4] {2}$
$=9\sqrt[4]{2}$
