Answer
sum is $15$; cannot easily be combined because the terms are unlike terms/radicals.
Work Step by Step
Extracting the root of the radicand, the given expression, $
\sqrt{64}+\sqrt[3]{125}+\sqrt[4]{16}
,$
simplifies to
\begin{align*}
&
\sqrt{8^2}+\sqrt[3]{5^3}+\sqrt[4]{2^4}
\\&=
8+5+2
\\&=
15
.\end{align*}
Thus, the sum of the given expression is $15$. Note that the expression cannot be combined easily because the terms are unlike radicals. Hence, it should be simplified first before the sum can be computed.
