Basic Math Examples

$4 \sqrt{12} \cdot \sqrt{54}$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$4 \sqrt{4 (3)} \cdot \sqrt{54}$

Step 1.2

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

$4 \sqrt{2^{2} \cdot 3} \cdot \sqrt{54}$

$4 \sqrt{2^{2} \cdot 3} \cdot \sqrt{54}$

Step 2

Pull terms out from under the radical.

$4 (2 \sqrt{3}) \cdot \sqrt{54}$

Step 3

Multiply $2$ by $4$ .

$8 \sqrt{3} \cdot \sqrt{54}$

Step 4

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 4.1

Factor $9$ out of $54$ .

$8 \sqrt{3} \cdot \sqrt{9 (6)}$

Step 4.2

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

$8 \sqrt{3} \cdot \sqrt{3^{2} \cdot 6}$

$8 \sqrt{3} \cdot \sqrt{3^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$8 \sqrt{3} \cdot (3 \sqrt{6})$

Step 6

Multiply $8 \sqrt{3} (3 \sqrt{6})$ .

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Step 6.1

Multiply $3$ by $8$ .

$24 \sqrt{3} \sqrt{6}$

Step 6.2

Combine using the product rule for radicals.

$24 \sqrt{6 \cdot 3}$

Step 6.3

Multiply $6$ by $3$ .

$24 \sqrt{18}$

$24 \sqrt{18}$

Step 7

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

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Step 7.1

Factor $9$ out of $18$ .

$24 \sqrt{9 (2)}$

Step 7.2

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

$24 \sqrt{3^{2} \cdot 2}$

$24 \sqrt{3^{2} \cdot 2}$

Step 8

Pull terms out from under the radical.

$24 (3 \sqrt{2})$

Step 9

Multiply $3$ by $24$ .

$72 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$72 \sqrt{2}$

Decimal Form:

$101.82337649 \dots$

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