Algebra Examples

$3 \sqrt{5 c^{3}} \cdot (7 \sqrt{15 c^{2}})$

Step 1

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

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Step 1.1

Factor out $c^{2}$ .

$3 \sqrt{5 (c^{2} c)} \cdot (7 \sqrt{15 c^{2}})$

Step 1.2

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

$3 \sqrt{c^{2} \cdot 5 c} \cdot (7 \sqrt{15 c^{2}})$

Step 1.3

Add parentheses.

$3 \sqrt{c^{2} \cdot (5 c)} \cdot (7 \sqrt{15 c^{2}})$

$3 \sqrt{c^{2} \cdot (5 c)} \cdot (7 \sqrt{15 c^{2}})$

Step 2

Pull terms out from under the radical.

$3 (c \sqrt{5 c}) \cdot (7 \sqrt{15 c^{2}})$

Step 3

Reorder $15$ and $c^{2}$ .

$3 c \sqrt{5 c} \cdot (7 \sqrt{c^{2} \cdot 15})$

Step 4

Pull terms out from under the radical.

$3 c \sqrt{5 c} \cdot (7 (c \sqrt{15}))$

Step 5

Multiply $c$ by $c$ by adding the exponents.

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Step 5.1

Move $c$ .

$3 (c \cdot c) \sqrt{5 c} \cdot (7 (\sqrt{15}))$

Step 5.2

Multiply $c$ by $c$ .

$3 c^{2} \sqrt{5 c} \cdot (7 (\sqrt{15}))$

$3 c^{2} \sqrt{5 c} \cdot (7 (\sqrt{15}))$

Step 6

Multiply $3 c^{2} \sqrt{5 c} (7 \sqrt{15})$ .

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Step 6.1

Multiply $7$ by $3$ .

$21 c^{2} \sqrt{5 c} \sqrt{15}$

Step 6.2

Combine using the product rule for radicals.

$21 c^{2} \sqrt{15 (5 c)}$

Step 6.3

Multiply $15$ by $5$ .

$21 c^{2} \sqrt{75 c}$

$21 c^{2} \sqrt{75 c}$

Step 7

Rewrite $75 c$ as $5^{2} \cdot (3 c)$ .

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Step 7.1

Factor $25$ out of $75$ .

$21 c^{2} \sqrt{25 (3) c}$

Step 7.2

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

$21 c^{2} \sqrt{5^{2} \cdot 3 c}$

Step 7.3

Add parentheses.

$21 c^{2} \sqrt{5^{2} \cdot (3 c)}$

$21 c^{2} \sqrt{5^{2} \cdot (3 c)}$

Step 8

Pull terms out from under the radical.

$21 c^{2} (5 \sqrt{3 c})$

Step 9

Multiply $5$ by $21$ .

$105 c^{2} \sqrt{3 c}$

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