Simplify square root of 8x^5y^6z^13

$\sqrt{8 x^{5} y^{6}} z^{13}$

Step 1

Rewrite $8 x^{5} y^{6}$ as ${(2 x^{2} y^{3})}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{5} y^{6}} z^{13}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2 x^{5} y^{6}} z^{13}$

Factor out $x^{4}$ .

$\sqrt{2^{2} \cdot 2 (x^{4} x) y^{6}} z^{13}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{2^{2} \cdot 2 ({(x^{2})}^{2} x) y^{6}} z^{13}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{2^{2} \cdot 2 ({(x^{2})}^{2} x) {(y^{3})}^{2}} z^{13}$

Move $x$ .

$\sqrt{2^{2} \cdot 2 ({(x^{2})}^{2}) {(y^{3})}^{2} x} z^{13}$

Move $2$ .

$\sqrt{(2^{2} ({(x^{2})}^{2})) {(y^{3})}^{2} \cdot 2 x} z^{13}$

Rewrite $(2^{2} ({(x^{2})}^{2})) {(y^{3})}^{2}$ as ${(2 x^{2} y^{3})}^{2}$ .

$\sqrt{{(2 x^{2} y^{3})}^{2} \cdot 2 x} z^{13}$

Add parentheses.

$\sqrt{{(2 x^{2} y^{3})}^{2} \cdot (2 x)} z^{13}$

Step 2

Pull terms out from under the radical.

$2 x^{2} y^{3} \sqrt{2 x} z^{13}$