Pre-Algebra Examples

$\sqrt{\frac{9}{81}}$

Step 1

Cancel the common factor of $9$ and $81$ .

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Step 1.1

Factor $9$ out of $9$ .

$\sqrt{\frac{9 (1)}{81}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $9$ out of $81$ .

$\sqrt{\frac{9 \cdot 1}{9 \cdot 9}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{9 \cdot 1}{9 \cdot 9}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{1}{9}}$

Step 2

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{\sqrt{1}}{\sqrt{9}}$

Step 3

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{9}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\frac{1}{\sqrt{3^{2}}}$

Step 4.2

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

$\frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$