Simplify square root of 50x^7y^14

$\sqrt{50 x^{7} y^{14}}$

Step 1

Rewrite $50 x^{7} y^{14}$ as ${(5 x^{3} y^{7})}^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{7} y^{14}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 x^{7} y^{14}}$

Factor out $x^{6}$ .

$\sqrt{5^{2} \cdot 2 (x^{6} x) y^{14}}$

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

$\sqrt{5^{2} \cdot 2 ({(x^{3})}^{2} x) y^{14}}$

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

$\sqrt{5^{2} \cdot 2 ({(x^{3})}^{2} x) {(y^{7})}^{2}}$

Move $x$ .

$\sqrt{5^{2} \cdot 2 ({(x^{3})}^{2}) {(y^{7})}^{2} x}$

Move $2$ .

$\sqrt{(5^{2} ({(x^{3})}^{2})) {(y^{7})}^{2} \cdot 2 x}$

Rewrite $(5^{2} ({(x^{3})}^{2})) {(y^{7})}^{2}$ as ${(5 x^{3} y^{7})}^{2}$ .

$\sqrt{{(5 x^{3} y^{7})}^{2} \cdot 2 x}$

Add parentheses.

$\sqrt{{(5 x^{3} y^{7})}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$5 x^{3} y^{7} \sqrt{2 x}$