# How do you simplify \sqrt { 49a ^ { 15} }?

May 1, 2018

$7 {a}^{7.5}$

#### Explanation:

As $49 = 7 \cdot 7 = {7}^{2}$,
$\sqrt{49} = 7$
And $\sqrt{{a}^{15}} = \sqrt{{a}^{14}} \cdot \sqrt{a} = {a}^{7} \sqrt{a} = {a}^{7.5}$
Multiplying the two, we get
$\sqrt{49 {a}^{15}} = 7 {a}^{7} \sqrt{a} = 7 {a}^{7.5}$
I think both $7 {a}^{7} \sqrt{a}$ and $7 {a}^{7.5}$ would be acceptable, and I cannot see any more simplification than this.