Basic Math Examples

$2 \sqrt{8} \cdot \sqrt{20}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$2 \sqrt{4 (2)} \cdot \sqrt{20}$

Step 1.2

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

$2 \sqrt{2^{2} \cdot 2} \cdot \sqrt{20}$

$2 \sqrt{2^{2} \cdot 2} \cdot \sqrt{20}$

Step 2

Pull terms out from under the radical.

$2 (2 \sqrt{2}) \cdot \sqrt{20}$

Step 3

Multiply $2$ by $2$ .

$4 \sqrt{2} \cdot \sqrt{20}$

Step 4

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

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Step 4.1

Factor $4$ out of $20$ .

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

Step 4.2

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

$4 \sqrt{2} \cdot \sqrt{2^{2} \cdot 5}$

$4 \sqrt{2} \cdot \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $4 \sqrt{2} (2 \sqrt{5})$ .

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Step 6.1

Multiply $2$ by $4$ .

$8 \sqrt{2} \sqrt{5}$

Step 6.2

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 2}$

Step 6.3

Multiply $5$ by $2$ .

$8 \sqrt{10}$

$8 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{10}$

Decimal Form:

$25.29822128 \dots$

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