Algebra Examples

$3 \sqrt{6}$ and $5 \sqrt{12}$

Step 1

Multiply the expressions.

$3 \sqrt{6} \cdot (5 \sqrt{12})$

Step 2

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

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Step 2.1

Factor $4$ out of $12$ .

$3 \sqrt{6} \cdot (5 \sqrt{4 (3)})$

Step 2.2

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

$3 \sqrt{6} \cdot (5 \sqrt{2^{2} \cdot 3})$

$3 \sqrt{6} \cdot (5 \sqrt{2^{2} \cdot 3})$

Step 3

Pull terms out from under the radical.

$3 \sqrt{6} \cdot (5 (2 \sqrt{3}))$

Step 4

Multiply $2$ by $5$ .

$3 \sqrt{6} \cdot (10 \sqrt{3})$

Step 5

Multiply $3 \sqrt{6} (10 \sqrt{3})$ .

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Step 5.1

Multiply $10$ by $3$ .

$30 \sqrt{6} \sqrt{3}$

Step 5.2

Combine using the product rule for radicals.

$30 \sqrt{3 \cdot 6}$

Step 5.3

Multiply $3$ by $6$ .

$30 \sqrt{18}$

$30 \sqrt{18}$

Step 6

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

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Step 6.1

Factor $9$ out of $18$ .

$30 \sqrt{9 (2)}$

Step 6.2

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

$30 \sqrt{3^{2} \cdot 2}$

$30 \sqrt{3^{2} \cdot 2}$

Step 7

Pull terms out from under the radical.

$30 (3 \sqrt{2})$

Step 8

Multiply $3$ by $30$ .

$90 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$90 \sqrt{2}$

Decimal Form:

$127.27922061 \dots$

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