Simplify square root of 50y^3

$\sqrt{50 y^{3}}$

Step 1

Rewrite $50 y^{3}$ as ${(5 y)}^{2} \cdot (2 y)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) y^{3}}$

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

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

Factor out $y^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$5 y \sqrt{2 y}$

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