Simplify square root of 48y^5

$\sqrt{48 y^{5}}$

Step 1

Rewrite $48 y^{5}$ as ${(4 y^{2})}^{2} \cdot (3 y)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) y^{5}}$

Rewrite $16$ as $4^{2}$ .

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

Factor out $y^{4}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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