Algebra Examples

$\frac{\sqrt{13}}{\sqrt{52}}$

Step 1

Combine $\sqrt{13}$ and $\sqrt{52}$ into a single radical.

$\sqrt{\frac{13}{52}}$

Step 2

Cancel the common factor of $13$ and $52$ .

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Step 2.1

Factor $13$ out of $13$ .

$\sqrt{\frac{13 (1)}{52}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $13$ out of $52$ .

$\sqrt{\frac{13 \cdot 1}{13 \cdot 4}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{13 \cdot 1}{13 \cdot 4}}$

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Any root of $1$ is $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$