Precalculus Examples

$\frac{\sqrt{18}}{\sqrt{81}}$

Step 1

Combine $\sqrt{18}$ and $\sqrt{81}$ into a single radical.

$\sqrt{\frac{18}{81}}$

Step 2

Cancel the common factor of $18$ and $81$ .

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Step 2.1

Factor $9$ out of $18$ .

$\sqrt{\frac{9 (2)}{81}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $9$ out of $81$ .

$\sqrt{\frac{9 \cdot 2}{9 \cdot 9}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{9 \cdot 2}{9 \cdot 9}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{2}{9}}$

Step 3

Rewrite $\sqrt{\frac{2}{9}}$ as $\frac{\sqrt{2}}{\sqrt{9}}$ .

$\frac{\sqrt{2}}{\sqrt{9}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.47140452 \dots$