Trigonometry Examples

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

Step 1

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

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

Step 2

Any root of $1$ is $1$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

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

Step 3.2

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

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

Step 4

Simplify terms.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 4.3

Combine $\frac{1}{2}$ and $\sqrt{2}$ .

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

Step 4.4

Simplify the expression.

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Step 4.4.1

Write $1$ as a fraction with a common denominator.

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

Step 4.4.2

Combine the numerators over the common denominator.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.29289321 \dots$