# How do you simplify sqrt (49 m^2n^ 8)?

Mar 27, 2018

$7 m {n}^{4}$

#### Explanation:

First, we know that $a \sqrt{b} c$ is the same as $a \sqrt{b} \cdot a \sqrt{c}$

Therefore, $\sqrt{49} {m}^{2} {n}^{8}$ is the same as $\sqrt{49} \cdot {\sqrt{m}}^{2} \cdot {\sqrt{n}}^{8}$

And we know that $\sqrt{49}$ is $7$ so we would have
$7 {\sqrt{m}}^{2} \cdot {\sqrt{n}}^{8}$

We also know that $a {\sqrt{b}}^{a}$ is the same as $b$, so ${\sqrt{m}}^{2}$ is $m$.

We would now have $7 m {\sqrt{n}}^{8}$.

We will apply the rule that $a {\sqrt{b}}^{c} = {b}^{\frac{c}{a}}$

So, $7 m {\sqrt{n}}^{8} = 7 m {n}^{\frac{8}{2}}$ and $\frac{8}{2}$ is $4$

Final answer: $7 m {n}^{4}$.