Answer
$\sqrt[4]{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[4]{405}-2\sqrt[4]{5}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[4]{81\cdot5}-2\sqrt[4]{5}
\\\\
\sqrt[4]{(3)^4\cdot5}-2\sqrt[4]{5}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
3\sqrt[4]{5}-2\sqrt[4]{5}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3-2)\sqrt[4]{5}
\\\\=
1\sqrt[4]{5}
\\\\=
\sqrt[4]{5}
.\end{array}