Simplify square root of 72x^3y^4

$\sqrt{72 x^{3} y^{4}}$

Step 1

Rewrite $72 x^{3} y^{4}$ as ${(6 x y^{2})}^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x^{3} y^{4}}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 x^{3} y^{4}}$

Factor out $x^{2}$ .

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

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$6 x y^{2} \sqrt{2 x}$