Algebra Examples

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

Step 1

Multiply $2$ by $2$ .

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

Step 2

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

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Step 2.1

Factor $4$ out of $20$ .

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

Step 2.2

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 5

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

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Step 5.1

Multiply $2$ by $4$ .

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

Step 5.2

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 2}$

Step 5.3

Multiply $5$ by $2$ .

$8 \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{10}$

Decimal Form:

$25.29822128 \dots$