Simplify square root of 45x^2y^5z^8

$\sqrt{45 x^{2} y^{5} z^{8}}$

Step 1

Rewrite $45 x^{2} y^{5} z^{8}$ as ${(3 x y^{2} z^{4})}^{2} \cdot (5 y)$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5) x^{2} y^{5} z^{8}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 5 x^{2} y^{5} z^{8}}$

Factor out $y^{4}$ .

$\sqrt{3^{2} \cdot 5 x^{2} (y^{4} y) z^{8}}$

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

$\sqrt{3^{2} \cdot 5 x^{2} ({(y^{2})}^{2} y) z^{8}}$

Rewrite $z^{8}$ as ${(z^{4})}^{2}$ .

$\sqrt{3^{2} \cdot 5 x^{2} ({(y^{2})}^{2} y) {(z^{4})}^{2}}$

Move $y$ .

$\sqrt{3^{2} \cdot 5 x^{2} ({(y^{2})}^{2}) {(z^{4})}^{2} y}$

Move $5$ .

$\sqrt{(3^{2} x^{2} ({(y^{2})}^{2})) {(z^{4})}^{2} \cdot 5 y}$

Rewrite $(3^{2} x^{2} ({(y^{2})}^{2})) {(z^{4})}^{2}$ as ${(3 x y^{2} z^{4})}^{2}$ .

$\sqrt{{(3 x y^{2} z^{4})}^{2} \cdot 5 y}$

Add parentheses.

$\sqrt{{(3 x y^{2} z^{4})}^{2} \cdot (5 y)}$

Step 2

Pull terms out from under the radical.

$3 x y^{2} z^{4} \sqrt{5 y}$