Trigonometry Examples

$\frac{7}{\frac{8}{- \sqrt{\frac{15}{64}}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$7 \frac{- \sqrt{\frac{15}{64}}}{8}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $\sqrt{\frac{15}{64}}$ as $\frac{\sqrt{15}}{\sqrt{64}}$ .

$7 \frac{- \frac{\sqrt{15}}{\sqrt{64}}}{8}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Rewrite $64$ as $8^{2}$ .

$7 \frac{- \frac{\sqrt{15}}{\sqrt{8^{2}}}}{8}$

Step 2.2.2

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

$7 \frac{- \frac{\sqrt{15}}{8}}{8}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$7 (- \frac{\sqrt{15}}{8} \cdot \frac{1}{8})$

Step 4

Multiply $- \frac{\sqrt{15}}{8} \cdot \frac{1}{8}$ .

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Step 4.1

Multiply $\frac{1}{8}$ by $\frac{\sqrt{15}}{8}$ .

$7 (- \frac{\sqrt{15}}{8 \cdot 8})$

Step 4.2

Multiply $8$ by $8$ .

$7 (- \frac{\sqrt{15}}{64})$

Step 5

Multiply $7 (- \frac{\sqrt{15}}{64})$ .

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Step 5.1

Multiply $- 1$ by $7$ .

$- 7 \frac{\sqrt{15}}{64}$

Step 5.2

Combine $- 7$ and $\frac{\sqrt{15}}{64}$ .

$\frac{- 7 \sqrt{15}}{64}$

Step 6

Move the negative in front of the fraction.

$- \frac{7 \sqrt{15}}{64}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 \sqrt{15}}{64}$

Decimal Form:

$- 0.42360755 \dots$