Basic Math Examples

$\sqrt{32} \cdot 4 \sqrt{75}$

Step 1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2)} \cdot (4 \sqrt{75})$

Step 1.2

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

$\sqrt{4^{2} \cdot 2} \cdot (4 \sqrt{75})$

$\sqrt{4^{2} \cdot 2} \cdot (4 \sqrt{75})$

Step 2

Pull terms out from under the radical.

$4 \sqrt{2} \cdot (4 \sqrt{75})$

Step 3

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 3.1

Factor $25$ out of $75$ .

$4 \sqrt{2} \cdot (4 \sqrt{25 (3)})$

Step 3.2

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

$4 \sqrt{2} \cdot (4 \sqrt{5^{2} \cdot 3})$

$4 \sqrt{2} \cdot (4 \sqrt{5^{2} \cdot 3})$

Step 4

Pull terms out from under the radical.

$4 \sqrt{2} \cdot (4 (5 \sqrt{3}))$

Step 5

Multiply $5$ by $4$ .

$4 \sqrt{2} \cdot (20 \sqrt{3})$

Step 6

Multiply $4 \sqrt{2} (20 \sqrt{3})$ .

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Step 6.1

Multiply $20$ by $4$ .

$80 \sqrt{2} \sqrt{3}$

Step 6.2

Combine using the product rule for radicals.

$80 \sqrt{3 \cdot 2}$

Step 6.3

Multiply $3$ by $2$ .

$80 \sqrt{6}$

$80 \sqrt{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{6}$

Decimal Form:

$195.95917942 \dots$

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