Basic Math Examples

$3 \sqrt{12} \cdot 3 \sqrt{6}$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.1

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)} \cdot (3 \sqrt{6})$

Step 1.2

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

$3 \sqrt{2^{2} \cdot 3} \cdot (3 \sqrt{6})$

$3 \sqrt{2^{2} \cdot 3} \cdot (3 \sqrt{6})$

Step 2

Pull terms out from under the radical.

$3 (2 \sqrt{3}) \cdot (3 \sqrt{6})$

Step 3

Multiply $2$ by $3$ .

$6 \sqrt{3} \cdot (3 \sqrt{6})$

Step 4

Multiply $6 \sqrt{3} (3 \sqrt{6})$ .

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Step 4.1

Multiply $3$ by $6$ .

$18 \sqrt{3} \sqrt{6}$

Step 4.2

Combine using the product rule for radicals.

$18 \sqrt{6 \cdot 3}$

Step 4.3

Multiply $6$ by $3$ .

$18 \sqrt{18}$

$18 \sqrt{18}$

Step 5

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 5.1

Factor $9$ out of $18$ .

$18 \sqrt{9 (2)}$

Step 5.2

Rewrite $9$ as $3^{2}$ .

$18 \sqrt{3^{2} \cdot 2}$

$18 \sqrt{3^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$18 (3 \sqrt{2})$

Step 7

Multiply $3$ by $18$ .

$54 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$54 \sqrt{2}$

Decimal Form:

$76.36753236 \dots$

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