Simplify square root of 90w^3y^4

$\sqrt{90 w^{3} y^{4}}$

Step 1

Rewrite $90 w^{3} y^{4}$ as ${(3 w y^{2})}^{2} \cdot (10 w)$ .

Factor $9$ out of $90$ .

$\sqrt{9 (10) w^{3} y^{4}}$

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

$\sqrt{3^{2} \cdot 10 w^{3} y^{4}}$

Factor out $w^{2}$ .

$\sqrt{3^{2} \cdot 10 (w^{2} w) y^{4}}$

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

$\sqrt{3^{2} \cdot 10 (w^{2} w) {(y^{2})}^{2}}$

Move $w$ .

$\sqrt{3^{2} \cdot 10 (w^{2}) {(y^{2})}^{2} w}$

Move $10$ .

$\sqrt{3^{2} (w^{2}) {(y^{2})}^{2} \cdot 10 w}$

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

$\sqrt{{(3 w y^{2})}^{2} \cdot 10 w}$

Add parentheses.

$\sqrt{{(3 w y^{2})}^{2} \cdot (10 w)}$

Step 2

Pull terms out from under the radical.

$3 w y^{2} \sqrt{10 w}$