# How do you simplify sqrt(16r^6)?

Jan 6, 2017

$4 {r}^{3}$

#### Explanation:

The trick is to look for squared value and then to take them outside the square root but not in squared form.

Note that $16 = {4}^{2} \text{ and } {r}^{6} = {r}^{3 \times 2} = {\left({r}^{3}\right)}^{2}$

$\sqrt{16 {r}^{6}} \text{ "->" "sqrt(4^2(r^3)^2)" "=" } 4 {r}^{3}$

If you wished to be really fussy consider this example:
$\left(- 2\right) \times \left(- 2\right) \text{ " =" " +4" " =" } \left(+ 2\right) \times \left(+ 2\right)$

So we have: $\sqrt{16 {r}^{6}} \text{ "->" "sqrt(4^2(r^3)^2)" "=" } \pm 4 {r}^{3}$

I suspect they are just looking for $+ 4 {r}^{3}$ as the answer