# How do you simplify sqrt(64b^48)?

Sep 30, 2015

It can be written as $8 {b}^{24}$

#### Explanation:

First if you have an expression like $\sqrt{a \cdot b}$ you can write it as $\sqrt{a} \cdot \sqrt{b}$, so you can write this as:

$\sqrt{64} \cdot \sqrt{{b}^{48}}$

Finally you can write $\sqrt{a}$ as ${a}^{\frac{1}{2}}$, so
$\sqrt{{b}^{48}} = {\left({b}^{48}\right)}^{\frac{1}{2}} = {b}^{\frac{48}{2}} = {b}^{24}$

Finally you get: $8 {b}^{24}$