Answer
$4\sqrt{3}-3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{48}-\dfrac{\sqrt{81}}{\sqrt{9}}
,$ simplify first each term by using the laws of radicals and by extracting the factor of the radicand that is a perfect power of the index. Then combine the like radicals.
$\bf{\text{Solution Details:}}$
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{48}-\sqrt{\dfrac{81}{9}}
\\\\=
\sqrt{48}-\sqrt{9}
.\end{array}
Rewriting 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{16\cdot3}-\sqrt{9}
\\\\=
\sqrt{(4)^2\cdot3}-\sqrt{(3)^2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
4\sqrt{3}-3
.\end{array}
