Simplify square root of 75x^4y^3

$\sqrt{75 x^{4} y^{3}}$

Step 1

Rewrite $75 x^{4} y^{3}$ as ${(5 x^{2} y)}^{2} \cdot (3 y)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{4} y^{3}}$

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

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

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

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

Factor out $y^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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