Simplify square root of 48y^7

$\sqrt{48 y^{7}}$

Step 1

Rewrite $48 y^{7}$ as ${(4 y^{3})}^{2} \cdot (3 y)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) y^{7}}$

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

$\sqrt{4^{2} \cdot 3 y^{7}}$

Factor out $y^{6}$ .

$\sqrt{4^{2} \cdot 3 (y^{6} y)}$

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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