Finite Math Examples

$4 \sqrt{2} \cdot (2 \sqrt{40})$

Step 1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 1.1

Factor $4$ out of $40$ .

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

Step 1.2

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $2$ .

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

Step 4

Multiply $4 \sqrt{2} (4 \sqrt{10})$ .

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Step 4.1

Multiply $4$ by $4$ .

$16 \sqrt{2} \sqrt{10}$

Step 4.2

Combine using the product rule for radicals.

$16 \sqrt{10 \cdot 2}$

Step 4.3

Multiply $10$ by $2$ .

$16 \sqrt{20}$

$16 \sqrt{20}$

Step 5

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

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Step 5.1

Factor $4$ out of $20$ .

$16 \sqrt{4 (5)}$

Step 5.2

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

$16 \sqrt{2^{2} \cdot 5}$

$16 \sqrt{2^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$16 (2 \sqrt{5})$

Step 7

Multiply $2$ by $16$ .

$32 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$32 \sqrt{5}$

Decimal Form:

$71.55417527 \dots$

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