Simplify 4y square root of 4x^4y^3

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

Step 1

Rewrite $4 x^{4} y^{3}$ as ${(2 x^{2} y)}^{2} y$ .

Rewrite $4$ as $2^{2}$ .

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

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

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

Factor out $y^{2}$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 4

Multiply $2$ by $4$ .

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

Step 5

Reorder factors in $8 y^{2} (x^{2} \sqrt{y})$ .

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