Simplify square root of 72x^5y^12

$\sqrt{72 x^{5} y^{12}}$

Step 1

Rewrite $72 x^{5} y^{12}$ as ${(6 x^{2} y^{6})}^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x^{5} y^{12}}$

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

$\sqrt{6^{2} \cdot 2 x^{5} y^{12}}$

Factor out $x^{4}$ .

$\sqrt{6^{2} \cdot 2 (x^{4} x) y^{12}}$

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

$\sqrt{6^{2} \cdot 2 ({(x^{2})}^{2} x) y^{12}}$

Rewrite $y^{12}$ as ${(y^{6})}^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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