# How do you simplify root3((y^2 - 1))?

Nov 5, 2015

This expression has no simpler form, but you can factor it:

$\sqrt[3]{{y}^{2} - 1} = \sqrt[3]{y - 1} \sqrt[3]{y + 1}$

#### Explanation:

The radicand ${y}^{2} - 1$ has no cubic factors, so there are no factors you can move out from under the cube root.

One thing you can do is separate the factors of ${y}^{2} - 1$, since $\sqrt[3]{a b} = \sqrt[3]{a} \sqrt[3]{b}$ ...

$\sqrt[3]{{y}^{2} - 1} = \sqrt[3]{\left(y - 1\right) \left(y + 1\right)} = \sqrt[3]{y - 1} \sqrt[3]{y + 1}$