Basic Math Examples

$3 \sqrt{5} \cdot (4 \sqrt{6}) \cdot \sqrt{15}$

Step 1

Multiply $3 \sqrt{5} (4 \sqrt{6})$ .

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Step 1.1

Multiply $4$ by $3$ .

$12 \sqrt{5} \sqrt{6} \cdot \sqrt{15}$

Step 1.2

Combine using the product rule for radicals.

$12 \sqrt{6 \cdot 5} \cdot \sqrt{15}$

Step 1.3

Multiply $6$ by $5$ .

$12 \sqrt{30} \cdot \sqrt{15}$

$12 \sqrt{30} \cdot \sqrt{15}$

Step 2

Multiply $12 \sqrt{30} \sqrt{15}$ .

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Step 2.1

Combine using the product rule for radicals.

$12 \sqrt{15 \cdot 30}$

Step 2.2

Multiply $15$ by $30$ .

$12 \sqrt{450}$

$12 \sqrt{450}$

Step 3

Rewrite $450$ as $15^{2} \cdot 2$ .

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Step 3.1

Factor $225$ out of $450$ .

$12 \sqrt{225 (2)}$

Step 3.2

Rewrite $225$ as $15^{2}$ .

$12 \sqrt{15^{2} \cdot 2}$

$12 \sqrt{15^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$12 (15 \sqrt{2})$

Step 5

Multiply $15$ by $12$ .

$180 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$180 \sqrt{2}$

Decimal Form:

$254.55844122 \dots$

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