# How do you simplify sqrt(32a^7b^4 )?

Oct 9, 2015

$4 {a}^{3} {b}^{2} \sqrt{2 a}$

#### Explanation:

Since everything under the square root is being multiplied, we can take out things that are squares. Let's break things up one piece at a time:

The $a$ variable:

$\sqrt{{a}^{7}}$
${a}^{6} \cdot a = {a}^{7}$
${a}^{3} \sqrt{a} = \sqrt{{a}^{7}}$

The $b$ variable:

$\sqrt{{b}^{4}}$
${b}^{2} = \sqrt{{b}^{4}}$

The constant (32):

$\sqrt{16 \cdot 2} = \sqrt{32}$
$4 \sqrt{2} = \sqrt{32}$

Now we multiply everything together in order to get our answer.
$4 {a}^{3} {b}^{2} \sqrt{2 a}$