Trigonometry Examples

$\sqrt{1 - \frac{\sqrt{39}}{\frac{8}{2}}}$

Step 1

Cancel the common factor of $8$ and $2$ .

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Step 1.1

Factor $2$ out of $8$ .

$\sqrt{1 - \frac{\sqrt{39}}{\frac{2 \cdot 4}{2}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\sqrt{1 - \frac{\sqrt{39}}{\frac{2 \cdot 4}{2 (1)}}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{1 - \frac{\sqrt{39}}{\frac{2 \cdot 4}{2 \cdot 1}}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{1 - \frac{\sqrt{39}}{\frac{4}{1}}}$

Step 1.2.4

Divide $4$ by $1$ .

$\sqrt{1 - \frac{\sqrt{39}}{4}}$

Step 2

Simplify the expression.

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Step 2.1

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

$\sqrt{\frac{4}{4} - \frac{\sqrt{39}}{4}}$

Step 2.2

Combine the numerators over the common denominator.

$\sqrt{\frac{4 - \sqrt{39}}{4}}$

Step 3

Rewrite $\sqrt{\frac{4 - \sqrt{39}}{4}}$ as $\frac{\sqrt{4 - \sqrt{39}}}{\sqrt{4}}$ .

$\frac{\sqrt{4 - \sqrt{39}}}{\sqrt{4}}$

Step 4

Simplify the denominator.

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Step 4.1

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

$\frac{\sqrt{4 - \sqrt{39}}}{\sqrt{2^{2}}}$

Step 4.2

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

$\frac{\sqrt{4 - \sqrt{39}}}{2}$