Answer
$2\sqrt{2}-2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{8}-\dfrac{\sqrt{64}}{\sqrt{16}}
,$ 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{8}-\sqrt{\dfrac{64}{16}}
\\\\=
\sqrt{8}-\sqrt{4}
.\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{4\cdot2}-\sqrt{4}
\\\\=
\sqrt{(2)^2\cdot2}-\sqrt{(2)^2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2\sqrt{2}-2
.\end{array}
