Trigonometry Examples

$\sqrt{\frac{\frac{3}{15}}{\frac{27}{15}}}$

Step 1

Cancel the common factor of $3$ and $15$ .

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Step 1.1

Factor $3$ out of $3$ .

$\sqrt{\frac{\frac{3 (1)}{15}}{\frac{27}{15}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $15$ .

$\sqrt{\frac{\frac{3 \cdot 1}{3 \cdot 5}}{\frac{27}{15}}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{\frac{3 \cdot 1}{3 \cdot 5}}{\frac{27}{15}}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{\frac{1}{5}}{\frac{27}{15}}}$

Step 2

Cancel the common factor of $27$ and $15$ .

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Step 2.1

Factor $3$ out of $27$ .

$\sqrt{\frac{\frac{1}{5}}{\frac{3 (9)}{15}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $15$ .

$\sqrt{\frac{\frac{1}{5}}{\frac{3 \cdot 9}{3 \cdot 5}}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{\frac{1}{5}}{\frac{3 \cdot 9}{3 \cdot 5}}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{\frac{1}{5}}{\frac{9}{5}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{1}{5} \cdot \frac{5}{9}}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$\sqrt{\frac{1}{5} \cdot \frac{5}{9}}$

Step 4.2

Rewrite the expression.

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

Step 5

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

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

Step 6

Any root of $1$ is $1$ .

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

Step 7

Simplify the denominator.

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Step 7.1

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

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

Step 7.2

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

$\frac{1}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$