Basic Math Examples

$\frac{6 \sqrt{6}}{2 \sqrt{24}}$

Step 1

Cancel the common factor of $6$ and $2$ .

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Step 1.1

Factor $2$ out of $6 \sqrt{6}$ .

$\frac{2 (3 \sqrt{6})}{2 \sqrt{24}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2 \sqrt{24}$ .

$\frac{2 (3 \sqrt{6})}{2 (\sqrt{24})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (3 \sqrt{6})}{2 \sqrt{24}}$

Step 1.2.3

Rewrite the expression.

$\frac{3 \sqrt{6}}{\sqrt{24}}$

Step 2

Combine $\sqrt{6}$ and $\sqrt{24}$ into a single radical.

$3 \sqrt{\frac{6}{24}}$

Step 3

Cancel the common factor of $6$ and $24$ .

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Step 3.1

Factor $6$ out of $6$ .

$3 \sqrt{\frac{6 (1)}{24}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $24$ .

$3 \sqrt{\frac{6 \cdot 1}{6 \cdot 4}}$

Step 3.2.2

Cancel the common factor.

$3 \sqrt{\frac{6 \cdot 1}{6 \cdot 4}}$

Step 3.2.3

Rewrite the expression.

$3 \sqrt{\frac{1}{4}}$

Step 4

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$3 \frac{\sqrt{1}}{\sqrt{4}}$

Step 5

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt{4}}$

Step 6

Simplify the denominator.

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Step 6.1

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

$3 \frac{1}{\sqrt{2^{2}}}$

Step 6.2

Pull terms out from under the radical, assuming positive real numbers.

$3 (\frac{1}{2})$

Step 7

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$