Simplify -3 square root of 45y^3

$- 3 \sqrt{45 y^{3}}$

Step 1

Rewrite $45 y^{3}$ as ${(3 y)}^{2} \cdot (5 y)$ .

Factor $9$ out of $45$ .

$- 3 \sqrt{9 (5) y^{3}}$

Rewrite $9$ as $3^{2}$ .

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

Factor out $y^{2}$ .

$- 3 \sqrt{3^{2} \cdot 5 (y^{2} y)}$

Move $5$ .

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

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

$- 3 \sqrt{{(3 y)}^{2} \cdot 5 y}$

Add parentheses.

$- 3 \sqrt{{(3 y)}^{2} \cdot (5 y)}$

$- 3 \sqrt{{(3 y)}^{2} \cdot (5 y)}$

Step 2

Pull terms out from under the radical.

$- 3 (3 y \sqrt{5 y})$

Step 3

Multiply $3$ by $- 3$ .

$- 9 y \sqrt{5 y}$

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