Simplify the Radical Expression - square root of 5q^3*3 square root of 35

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

Step 1

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.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $3$ by $- 1$ .

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

Step 4

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

Combine using the product rule for radicals.

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

Multiply $35$ by $5$ .

$- 3 | q | \sqrt{175 q}$

Step 5

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.

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

Step 6

Pull terms out from under the radical.

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

Step 7

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

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

Step 8

Multiply $5$ by $- 3$ .

$- 15 | q | \sqrt{7 q}$