Answer
$3,125$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents to convert the given expression, $
\sqrt{5^{10}}
,$ to exponential form.
$\bf{\text{Solution Details:}}$
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[2]{5^{10}}
\\\\=
5^{\frac{10}{2}}
\\\\=
5^{5}
\\\\=
3,125
.\end{array}