Answer
$-27\sqrt{2}$
Work Step by Step
Extracting the factor that is a perfect root of the radical, the given expression, $
2\sqrt{32}-5\sqrt{98}
$, is equivalent to
\begin{align*}
&
2\sqrt{16\cdot2}-5\sqrt{49\cdot2}
\\&=
2\sqrt{16}\cdot\sqrt{2}-5\sqrt{49}\cdot\sqrt{2}
\\&=
2(4)\cdot\sqrt{2}-5(7)\cdot\sqrt{2}
\\&=
8\sqrt{2}-35\sqrt{2}
.\end{align*}
Combining like radicals, the expression above is equivalent to
\begin{align*}
&
(8-35)\sqrt{2}
\\&=
-27\sqrt{2}
.\end{align*}
Hence, the expression $
2\sqrt{32}-5\sqrt{98}
$ simplifies to $
-27\sqrt{2}
$.
