Pre-Algebra Examples

$\frac{2 \sqrt{18}}{6 \sqrt{6}}$

Step 1

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

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Step 1.1

Factor $2$ out of $2 \sqrt{18}$ .

$\frac{2 (\sqrt{18})}{6 \sqrt{6}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

$\frac{2 (\sqrt{18})}{2 (3 \sqrt{6})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 \sqrt{18}}{2 (3 \sqrt{6})}$

Step 1.2.3

Rewrite the expression.

$\frac{\sqrt{18}}{3 \sqrt{6}}$

$\frac{\sqrt{18}}{3 \sqrt{6}}$

$\frac{\sqrt{18}}{3 \sqrt{6}}$

Step 2

Combine $\sqrt{18}$ and $\sqrt{6}$ into a single radical.

$\frac{\sqrt{\frac{18}{6}}}{3}$

Step 3

Cancel the common factor of $18$ and $6$ .

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Step 3.1

Factor $6$ out of $18$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $6$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $3$ by $1$ .

$\frac{\sqrt{3}}{3}$

$\frac{\sqrt{3}}{3}$

$\frac{\sqrt{3}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{3}$

Decimal Form:

$0.57735026 \dots$

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