Pre-Algebra Examples

$\frac{\sqrt{3}}{\sqrt{75}}$

Step 1

Combine $\sqrt{3}$ and $\sqrt{75}$ into a single radical.

$\sqrt{\frac{3}{75}}$

Step 2

Cancel the common factor of $3$ and $75$ .

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Step 2.1

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (1)}{75}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $75$ .

$\sqrt{\frac{3 \cdot 1}{3 \cdot 25}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 1}{3 \cdot 25}}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

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

Step 4

Any root of $1$ is $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $25$ as $5^{2}$ .

$\frac{1}{\sqrt{5^{2}}}$

Step 5.2

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

$\frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$