Simplify - square root of 5q^3*3 square root of 35

$- \sqrt{5 q^{3}} \cdot 3 \sqrt{35}$

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

Factor out $q^{2}$ .

$- \sqrt{5 (q^{2} q)} \cdot (3 \sqrt{35})$

Reorder $5$ and $q^{2}$ .

$- \sqrt{q^{2} \cdot 5 q} \cdot (3 \sqrt{35})$

Add parentheses.

$- \sqrt{q^{2} \cdot (5 q)} \cdot (3 \sqrt{35})$

$- \sqrt{q^{2} \cdot (5 q)} \cdot (3 \sqrt{35})$

Pull terms out from under the radical.

$- (q \sqrt{5 q}) \cdot (3 \sqrt{35})$

Multiply $- q \sqrt{5 q} (3 \sqrt{35})$ .

Multiply $3$ by $- 1$ .

$- 3 q \sqrt{5 q} \sqrt{35}$

Combine using the product rule for radicals.

$- 3 q \sqrt{35 (5 q)}$

Multiply $35$ by $5$ .

$- 3 q \sqrt{175 q}$

$- 3 q \sqrt{175 q}$

Rewrite $175 q$ as $5^{2} \cdot (7 q)$ .

Factor $25$ out of $175$ .

$- 3 q \sqrt{25 (7) q}$

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

$- 3 q \sqrt{5^{2} \cdot 7 q}$

Add parentheses.

$- 3 q \sqrt{5^{2} \cdot (7 q)}$

$- 3 q \sqrt{5^{2} \cdot (7 q)}$

Pull terms out from under the radical.

$- 3 q (5 \sqrt{7 q})$

Multiply $5$ by $- 3$ .

$- 15 q \sqrt{7 q}$

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