Basic Math Examples

$(4 \sqrt{10}) (- 3 \sqrt{2})$

Step 1

Multiply $(4 \sqrt{10}) (- 3 \sqrt{2})$ .

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Step 1.1

Multiply $- 3$ by $4$ .

$- 12 \sqrt{10} \sqrt{2}$

Step 1.2

Combine using the product rule for radicals.

$- 12 \sqrt{2 \cdot 10}$

Step 1.3

Multiply $2$ by $10$ .

$- 12 \sqrt{20}$

$- 12 \sqrt{20}$

Step 2

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 2.1

Factor $4$ out of $20$ .

$- 12 \sqrt{4 (5)}$

Step 2.2

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

$- 12 \sqrt{2^{2} \cdot 5}$

$- 12 \sqrt{2^{2} \cdot 5}$

Step 3

Pull terms out from under the radical.

$- 12 (2 \sqrt{5})$

Step 4

Multiply $2$ by $- 12$ .

$- 24 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 24 \sqrt{5}$

Decimal Form:

$- 53.66563145 \dots$

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