Simplify 3 square root of 5y* square root of 6y* square root of 12y

$3 \sqrt{5 y} \cdot \sqrt{6 y} \cdot \sqrt{12 y}$

Multiply $3 \sqrt{5 y} \sqrt{6 y}$ .

Combine using the product rule for radicals.

$3 \sqrt{6 y (5 y)} \cdot \sqrt{12 y}$

Multiply $5$ by $6$ .

$3 \sqrt{30 y \cdot y} \cdot \sqrt{12 y}$

Raise $y$ to the power of $1$ .

$3 \sqrt{30 (y^{1} y)} \cdot \sqrt{12 y}$

Raise $y$ to the power of $1$ .

$3 \sqrt{30 (y^{1} y^{1})} \cdot \sqrt{12 y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \sqrt{30 y^{1 + 1}} \cdot \sqrt{12 y}$

Add $1$ and $1$ .

$3 \sqrt{30 y^{2}} \cdot \sqrt{12 y}$

$3 \sqrt{30 y^{2}} \cdot \sqrt{12 y}$

Reorder $30$ and $y^{2}$ .

$3 \sqrt{y^{2} \cdot 30} \cdot \sqrt{12 y}$

Pull terms out from under the radical.

$3 (y \sqrt{30}) \cdot \sqrt{12 y}$

Rewrite $12 y$ as $2^{2} \cdot (3 y)$ .

Factor $4$ out of $12$ .

$3 y \sqrt{30} \cdot \sqrt{4 (3) y}$

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

$3 y \sqrt{30} \cdot \sqrt{2^{2} \cdot 3 y}$

Add parentheses.

$3 y \sqrt{30} \cdot \sqrt{2^{2} \cdot (3 y)}$

$3 y \sqrt{30} \cdot \sqrt{2^{2} \cdot (3 y)}$

Pull terms out from under the radical.

$3 y \sqrt{30} \cdot (2 \sqrt{3 y})$

Multiply $3 y \sqrt{30} (2 \sqrt{3 y})$ .

Multiply $2$ by $3$ .

$6 y \sqrt{30} \sqrt{3 y}$

Combine using the product rule for radicals.

$6 y \sqrt{3 y \cdot 30}$

Multiply $30$ by $3$ .

$6 y \sqrt{90 y}$

$6 y \sqrt{90 y}$

Rewrite $90 y$ as $3^{2} \cdot (10 y)$ .

Factor $9$ out of $90$ .

$6 y \sqrt{9 (10) y}$

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

$6 y \sqrt{3^{2} \cdot 10 y}$

Add parentheses.

$6 y \sqrt{3^{2} \cdot (10 y)}$

$6 y \sqrt{3^{2} \cdot (10 y)}$

Pull terms out from under the radical.

$6 y (3 \sqrt{10 y})$

Multiply $3$ by $6$ .

$18 y \sqrt{10 y}$

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