Algebra Examples

$\sqrt{\frac{6}{8}} \cdot \sqrt{\frac{6}{18}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{6}{8} \cdot \frac{6}{18}}$

Step 2

Multiply $\frac{6}{8}$ by $\frac{6}{18}$ .

$\sqrt{\frac{6 \cdot 6}{8 \cdot 18}}$

Step 3

Reduce the expression $\frac{6 \cdot 6}{8 \cdot 18}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $6 \cdot 6$ .

$\sqrt{\frac{2 (3 \cdot 6)}{8 \cdot 18}}$

Step 3.2

Factor $2$ out of $8 \cdot 18$ .

$\sqrt{\frac{2 (3 \cdot 6)}{2 (4 \cdot 18)}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{2 (3 \cdot 6)}{2 (4 \cdot 18)}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{3 \cdot 6}{4 \cdot 18}}$

$\sqrt{\frac{3 \cdot 6}{4 \cdot 18}}$

Step 4

Cancel the common factor of $3$ and $18$ .

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Step 4.1

Factor $3$ out of $3 \cdot 6$ .

$\sqrt{\frac{3 (6)}{4 \cdot 18}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $4 \cdot 18$ .

$\sqrt{\frac{3 (6)}{3 (4 \cdot 6)}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 6}{3 (4 \cdot 6)}}$

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $6$ and $4$ .

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Step 5.1

Factor $2$ out of $6$ .

$\sqrt{\frac{2 (3)}{4 \cdot 6}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $4 \cdot 6$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\sqrt{\frac{3}{2 \cdot 6}}$

$\sqrt{\frac{3}{2 \cdot 6}}$

$\sqrt{\frac{3}{2 \cdot 6}}$

Step 6

Cancel the common factor of $3$ and $6$ .

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Step 6.1

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (1)}{2 \cdot 6}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $2 \cdot 6$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\sqrt{\frac{1}{2 \cdot 2}}$

$\sqrt{\frac{1}{2 \cdot 2}}$

$\sqrt{\frac{1}{2 \cdot 2}}$

Step 7

Multiply $2$ by $2$ .

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

Step 8

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

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

Step 9

Any root of $1$ is $1$ .

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

Step 10

Simplify the denominator.

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Step 10.1

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

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

Step 10.2

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

$\frac{1}{2}$

$\frac{1}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

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