Basic Math Examples

$\sqrt{5 c^{4}} \sqrt{20 c}$

Step 1

Rewrite $5 c^{4}$ as ${(c^{2})}^{2} \cdot 5$ .

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Step 1.1

Rewrite $c^{4}$ as ${(c^{2})}^{2}$ .

$\sqrt{5 {(c^{2})}^{2}} \sqrt{20 c}$

Step 1.2

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

$\sqrt{{(c^{2})}^{2} \cdot 5} \sqrt{20 c}$

$\sqrt{{(c^{2})}^{2} \cdot 5} \sqrt{20 c}$

Step 2

Pull terms out from under the radical.

$c^{2} \sqrt{5} \sqrt{20 c}$

Step 3

Rewrite $20 c$ as $2^{2} \cdot (5 c)$ .

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Step 3.1

Factor $4$ out of $20$ .

$c^{2} \sqrt{5} \sqrt{4 (5) c}$

Step 3.2

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

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

Step 3.3

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Combine using the product rule for radicals.

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

Step 5.2

Multiply $5$ by $5$ .

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

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

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$2 c^{2} \sqrt{25 c}$

Step 6.2

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

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

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

Step 7

Pull terms out from under the radical.

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

Step 8

Multiply $5$ by $2$ .

$10 c^{2} \sqrt{c}$

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