Basic Math Examples

$\sqrt{8 v^{2}} \cdot \sqrt{10 v}$

Step 1

Rewrite $8 v^{2}$ as ${(2 v)}^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) v^{2}} \cdot \sqrt{10 v}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2 v^{2}} \cdot \sqrt{10 v}$

Step 1.3

Move $2$ .

$\sqrt{2^{2} v^{2} \cdot 2} \cdot \sqrt{10 v}$

Step 1.4

Rewrite $2^{2} v^{2}$ as ${(2 v)}^{2}$ .

$\sqrt{{(2 v)}^{2} \cdot 2} \cdot \sqrt{10 v}$

$\sqrt{{(2 v)}^{2} \cdot 2} \cdot \sqrt{10 v}$

Step 2

Pull terms out from under the radical.

$2 v \sqrt{2} \cdot \sqrt{10 v}$

Step 3

Multiply $2 v \sqrt{2} \sqrt{10 v}$ .

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Step 3.1

Combine using the product rule for radicals.

$2 v \sqrt{10 v \cdot 2}$

Step 3.2

Multiply $2$ by $10$ .

$2 v \sqrt{20 v}$

$2 v \sqrt{20 v}$

Step 4

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

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Step 4.1

Factor $4$ out of $20$ .

$2 v \sqrt{4 (5) v}$

Step 4.2

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

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

Step 4.3

Add parentheses.

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

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

Step 5

Pull terms out from under the radical.

$2 v (2 \sqrt{5 v})$

Step 6

Multiply $2$ by $2$ .

$4 v \sqrt{5 v}$

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