Simplify square root of 75x^7y^5

$\sqrt{75 x^{7} y^{5}}$

Step 1

Rewrite $75 x^{7} y^{5}$ as ${(5 x^{3} y^{2})}^{2} \cdot (3 x y)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{7} y^{5}}$

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

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

Factor out $x^{6}$ .

$\sqrt{5^{2} \cdot 3 (x^{6} x) y^{5}}$

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

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

Factor out $y^{4}$ .

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

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

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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