Answer
$\sqrt{7}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{7}{\sqrt{7}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{7}{\sqrt{7}}\cdot\dfrac{\sqrt{7}}{\sqrt{7}}
\\\\=
\dfrac{7\sqrt{7}}{\sqrt{7}(\sqrt{7})}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{7\sqrt{7}}{\sqrt{7(7)}}
\\\\=
\dfrac{7\sqrt{7}}{\sqrt{7^2}}
\\\\=
\dfrac{7\sqrt{7}}{7}
\\\\=
\dfrac{\cancel{7}\sqrt{7}}{\cancel{7}}
\\\\=
\sqrt{7}
.\end{array}
