Algebra Examples

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

Step 1

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

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Step 1.1

Factor $4$ out of $20$ .

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

Step 1.2

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $2$ .

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

Step 4

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

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Step 4.1

Multiply $4$ by $2$ .

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

Step 4.2

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 2}$

Step 4.3

Multiply $5$ by $2$ .

$8 \sqrt{10}$

$8 \sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{10}$

Decimal Form:

$25.29822128 \dots$

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