Dividing and Simplifying Radical Expressions
Note that ![\frac{\sqrt[3]{27}} {\sqrt[3]{8}}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-54990075bf15138f3d02d54558051370_l3.png "Rendered by QuickLaTeX.com")
=
and that ![\sqrt[a]{\frac{27}{8}}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-05bab2f8f8db71ee55af57c2cdd60597_l3.png "Rendered by QuickLaTeX.com")
= . This example suggests the following.
The Quotient Rule For Radicals
For any nonnegative number a, any positive number b, and any index k,
![\frac{\sqrt[k]{a}}{\sqrt[k]{b}}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-bde6ad3c6a1b21eb9347d725e31ccea2_l3.png "Rendered by QuickLaTeX.com")
= ![\sqrt[k]{\frac{a}{b}}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-f044ddc0d1ddf6f96a549d19db6a4aae_l3.png "Rendered by QuickLaTeX.com")
, or 
.
(To divide, divide the radicands. After doing this, you can sometimes simplify by taking roots.)