Algebra Examples

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

Step 1

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

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Step 1.1

Factor out $q^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Multiply $3$ by $- 1$ .

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

Step 3.2

Combine using the product rule for radicals.

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

Step 3.3

Multiply $35$ by $5$ .

$- 3 q \sqrt{175 q}$

$- 3 q \sqrt{175 q}$

Step 4

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

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Step 4.1

Factor $25$ out of $175$ .

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

Step 4.2

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

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

Step 4.3

Add parentheses.

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $5$ by $- 3$ .

$- 15 q \sqrt{7 q}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$