Basic Math Examples

$- 12 \sqrt{24} \div 3 \sqrt{2}$

Step 1

Rewrite the division as a fraction.

$\frac{- 12 \sqrt{24}}{3 \sqrt{2}}$

Step 2

Cancel the common factor of $- 12$ and $3$ .

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Step 2.1

Factor $3$ out of $- 12 \sqrt{24}$ .

$\frac{3 (- 4 \sqrt{24})}{3 \sqrt{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3 \sqrt{2}$ .

$\frac{3 (- 4 \sqrt{24})}{3 (\sqrt{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (- 4 \sqrt{24})}{3 \sqrt{2}}$

Step 2.2.3

Rewrite the expression.

$\frac{- 4 \sqrt{24}}{\sqrt{2}}$

$\frac{- 4 \sqrt{24}}{\sqrt{2}}$

$\frac{- 4 \sqrt{24}}{\sqrt{2}}$

Step 3

Combine $\sqrt{24}$ and $\sqrt{2}$ into a single radical.

$- 4 \sqrt{\frac{24}{2}}$

Step 4

Divide $24$ by $2$ .

$- 4 \sqrt{12}$

Step 5

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

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Step 5.1

Factor $4$ out of $12$ .

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

Step 5.2

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

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $2$ by $- 4$ .

$- 8 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 8 \sqrt{3}$

Decimal Form:

$- 13.85640646 \dots$

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