Trigonometry Examples

\sqrt{\frac{1 - 2 (\frac{1}{4})}{2}}

$\sqrt{\frac{1 - 2 (\frac{1}{4})}{2}}$

Step 1

Cancel the common factor of

2

$2$ .

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Step 1.1

Factor

2

$2$ out of

- 2

$- 2$ .

\sqrt{\frac{1 + 2 (- 1) \frac{1}{4}}{2}}

$\sqrt{\frac{1 + 2 (- 1) \frac{1}{4}}{2}}$

Step 1.2

Factor

2

$2$ out of

4

$4$ .

\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}

$\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}$

Step 1.3

Cancel the common factor.

\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}

$\sqrt{\frac{1 + 2 \cdot - 1 \frac{1}{2 \cdot 2}}{2}}$

Step 1.4

Rewrite the expression.

\sqrt{\frac{1 - 1 (\frac{1}{2})}{2}}

$\sqrt{\frac{1 - 1 (\frac{1}{2})}{2}}$

\sqrt{\frac{1 - 1 (\frac{1}{2})}{2}}

$\sqrt{\frac{1 - 1 (\frac{1}{2})}{2}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite

- 1 (\frac{1}{2})

$- 1 (\frac{1}{2})$ as

- (\frac{1}{2})

$- (\frac{1}{2})$ .

\sqrt{\frac{1 - (\frac{1}{2})}{2}}

$\sqrt{\frac{1 - (\frac{1}{2})}{2}}$

Step 2.2

Write

1

$1$ as a fraction with a common denominator.

\sqrt{\frac{\frac{2}{2} - \frac{1}{2}}{2}}

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

Step 2.3

Combine the numerators over the common denominator.

\sqrt{\frac{\frac{2 - 1}{2}}{2}}

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

Step 2.4

Subtract

1

$1$ from

2

$2$ .

\sqrt{\frac{\frac{1}{2}}{2}}

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

\sqrt{\frac{\frac{1}{2}}{2}}

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

\sqrt{\frac{1}{2} \cdot \frac{1}{2}}

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

Step 4

Multiply

\frac{1}{2} \cdot \frac{1}{2}

$\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 4.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{1}{2}

$\frac{1}{2}$ .

\sqrt{\frac{1}{2 \cdot 2}}

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

Step 4.2

Multiply

2

$2$ by

2

$2$ .

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

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

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

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

Step 5

Rewrite

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

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

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

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

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

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

Step 6

Any root of

1

$1$ is

1

$1$ .

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

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

Step 7

Simplify the denominator.

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Step 7.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 7.2

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

\frac{1}{2}

$\frac{1}{2}$

\frac{1}{2}

$\frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{1}{2}

$\frac{1}{2}$

Decimal Form:

0.5

$0.5$