# How do divide radical expressions?

Mar 22, 2015

If the radicals are of the same power, then they can be combined under a common radical sign
$\frac{\sqrt[a]{p}}{\sqrt[a]{q}} = \sqrt[a]{\frac{p}{q}}$

e.q.
$\frac{\sqrt[2]{27}}{\sqrt[2]{75}} = \sqrt[2]{\frac{27}{75}} = \sqrt[2]{\frac{\left(3\right) \left(9\right)}{\left(3\right) \left(25\right)}} = \frac{3}{4}$

If the radicals are of different powers:
$\left(\sqrt[a]{p}\right) = \left(\sqrt[b]{q}\right)$

$\rightarrow \frac{\sqrt[a \cdot b]{{p}^{b}}}{\sqrt[a \cdot b]{{q}^{a}}}$

$\rightarrow \sqrt[a \cdot b]{{p}^{b} / {q}^{a}}$