Simplify square root of 384x^4y^3

$\sqrt{384 x^{4} y^{3}}$

Step 1

Rewrite $384 x^{4} y^{3}$ as ${(8 x^{2} y)}^{2} \cdot (6 y)$ .

Factor $64$ out of $384$ .

$\sqrt{64 (6) x^{4} y^{3}}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 6 x^{4} y^{3}}$

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

$\sqrt{8^{2} \cdot 6 {(x^{2})}^{2} y^{3}}$

Factor out $y^{2}$ .

$\sqrt{8^{2} \cdot 6 {(x^{2})}^{2} (y^{2} y)}$

Move $6$ .

$\sqrt{8^{2} {(x^{2})}^{2} y^{2} \cdot 6 y}$

Rewrite $8^{2} {(x^{2})}^{2} y^{2}$ as ${(8 x^{2} y)}^{2}$ .

$\sqrt{{(8 x^{2} y)}^{2} \cdot 6 y}$

Add parentheses.

$\sqrt{{(8 x^{2} y)}^{2} \cdot (6 y)}$

Step 2

Pull terms out from under the radical.

$8 x^{2} y \sqrt{6 y}$