Algebra Examples

$\sqrt{\frac{25}{100}}$

Step 1

Cancel the common factor of $25$ and $100$ .

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Step 1.1

Factor $25$ out of $25$ .

$\sqrt{\frac{25 (1)}{100}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $25$ out of $100$ .

$\sqrt{\frac{25 \cdot 1}{25 \cdot 4}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{25 \cdot 1}{25 \cdot 4}}$

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Any root of $1$ is $1$ .

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

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$