Answer
$4\sqrt{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{50}-\sqrt{98}+\sqrt{72}
,$ simplify each term by extracting the root of the factor that is a perfect power of the index. Then combine like terms.
$\bf{\text{Solution Details:}}$
Writing the radicand as an expression that contains a factor that is a perfect power of the index and extracting the root of that factor result to
\begin{array}{l}\require{cancel}
\sqrt{25\cdot2}-\sqrt{49\cdot2}+\sqrt{36\cdot2}
\\\\=
\sqrt{(5)^2\cdot2}-\sqrt{(7)^2\cdot2}+\sqrt{(6)^2\cdot2}
\\\\=
5\sqrt{2}-7\sqrt{2}+6\sqrt{2}
.\end{array}
By combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(5-7+6)\sqrt{2}
\\\\=
4\sqrt{2}
.\end{array}
