Basic Math Examples

$4 \sqrt{50} \cdot \sqrt{80}$

Step 1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.1

Factor $25$ out of $50$ .

$4 \sqrt{25 (2)} \cdot \sqrt{80}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{5^{2} \cdot 2} \cdot \sqrt{80}$

$4 \sqrt{5^{2} \cdot 2} \cdot \sqrt{80}$

Step 2

Pull terms out from under the radical.

$4 (5 \sqrt{2}) \cdot \sqrt{80}$

Step 3

Multiply $5$ by $4$ .

$20 \sqrt{2} \cdot \sqrt{80}$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 4.1

Factor $16$ out of $80$ .

$20 \sqrt{2} \cdot \sqrt{16 (5)}$

Step 4.2

Rewrite $16$ as $4^{2}$ .

$20 \sqrt{2} \cdot \sqrt{4^{2} \cdot 5}$

$20 \sqrt{2} \cdot \sqrt{4^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$20 \sqrt{2} \cdot (4 \sqrt{5})$

Step 6

Multiply $20 \sqrt{2} (4 \sqrt{5})$ .

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Step 6.1

Multiply $4$ by $20$ .

$80 \sqrt{2} \sqrt{5}$

Step 6.2

Combine using the product rule for radicals.

$80 \sqrt{5 \cdot 2}$

Step 6.3

Multiply $5$ by $2$ .

$80 \sqrt{10}$

$80 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{10}$

Decimal Form:

$252.98221281 \dots$

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