Algebra Examples

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

Step 1

Multiply $3$ by $2$ .

$6 \sqrt{5} \sqrt{2} \cdot \sqrt{6}$

Step 2

Multiply $6 \sqrt{5} \sqrt{2}$ .

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Step 2.1

Combine using the product rule for radicals.

$6 \sqrt{2 \cdot 5} \cdot \sqrt{6}$

Step 2.2

Multiply $2$ by $5$ .

$6 \sqrt{10} \cdot \sqrt{6}$

Step 3

Multiply $6 \sqrt{10} \sqrt{6}$ .

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Step 3.1

Combine using the product rule for radicals.

$6 \sqrt{6 \cdot 10}$

Step 3.2

Multiply $6$ by $10$ .

$6 \sqrt{60}$

Step 4

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 4.1

Factor $4$ out of $60$ .

$6 \sqrt{4 (15)}$

Step 4.2

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

$6 \sqrt{2^{2} \cdot 15}$

Step 5

Pull terms out from under the radical.

$6 (| 2 | \sqrt{15})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$6 (2 \sqrt{15})$

Step 7

Multiply $2$ by $6$ .

$12 \sqrt{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{15}$

Decimal Form:

$46.47580015 \dots$