Question

simplify 4√6/√30 by rationalizing the denominator. show your work

Answer 1

\[\frac{4\sqrt{6}}{\sqrt{30}} = \frac{4\sqrt{6}\times \sqrt{30}}{\sqrt{30} \times \sqrt{30}}\]
\[\frac{4 \sqrt{180}}{30} = \frac{4 \sqrt{4 \times 9 \times 5}}{30} = \frac{4 \times 2 \times 3 \sqrt{5}}{30}\]
\[= \frac{4\sqrt{5}}{5}\]

Answer 2

For your edification, the general technique to rationalize the denominator of something of the form \(\frac{a}{\sqrt b}\) is as follows.\[\Large \frac{a}{\sqrt b}=\frac{a}{\sqrt b}\cdot\frac{\sqrt b}{\sqrt b}=\frac{a\sqrt b}{b}\]