Trigonometry Examples

$\frac{- 64 - \sqrt{96}}{- 36}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $96$ as $4^{2} \cdot 6$ .

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Step 1.1.1

Factor $16$ out of $96$ .

$\frac{- 64 - \sqrt{16 (6)}}{- 36}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{- 64 - \sqrt{4^{2} \cdot 6}}{- 36}$

$\frac{- 64 - \sqrt{4^{2} \cdot 6}}{- 36}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 64 - (4 \sqrt{6})}{- 36}$

Step 1.3

Multiply $4$ by $- 1$ .

$\frac{- 64 - 4 \sqrt{6}}{- 36}$

$\frac{- 64 - 4 \sqrt{6}}{- 36}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- 64 - 4 \sqrt{6}$ and $- 36$ .

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Step 2.1.1

Factor $4$ out of $- 64$ .

$\frac{4 (- 16) - 4 \sqrt{6}}{- 36}$

Step 2.1.2

Factor $4$ out of $- 4 \sqrt{6}$ .

$\frac{4 (- 16) + 4 (- \sqrt{6})}{- 36}$

Step 2.1.3

Factor $4$ out of $4 (- 16) + 4 (- \sqrt{6})$ .

$\frac{4 (- 16 - \sqrt{6})}{- 36}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $4$ out of $- 36$ .

$\frac{4 (- 16 - \sqrt{6})}{4 \cdot - 9}$

Step 2.1.4.2

Cancel the common factor.

$\frac{4 (- 16 - \sqrt{6})}{4 \cdot - 9}$

Step 2.1.4.3

Rewrite the expression.

$\frac{- 16 - \sqrt{6}}{- 9}$

$\frac{- 16 - \sqrt{6}}{- 9}$

$\frac{- 16 - \sqrt{6}}{- 9}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{- 16 - \sqrt{6}}{9}$

Step 2.3

Rewrite $- 16$ as $- 1 (16)$ .

$- \frac{- 1 (16) - \sqrt{6}}{9}$

Step 2.4

Factor $- 1$ out of $- \sqrt{6}$ .

$- \frac{- 1 (16) - (\sqrt{6})}{9}$

Step 2.5

Factor $- 1$ out of $- 1 (16) - (\sqrt{6})$ .

$- \frac{- 1 (16 + \sqrt{6})}{9}$

Step 2.6

Simplify the expression.

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Step 2.6.1

Move the negative in front of the fraction.

$- - \frac{16 + \sqrt{6}}{9}$

Step 2.6.2

Multiply $- 1$ by $- 1$ .

$1 \frac{16 + \sqrt{6}}{9}$

Step 2.6.3

Multiply $\frac{16 + \sqrt{6}}{9}$ by $1$ .

$\frac{16 + \sqrt{6}}{9}$

$\frac{16 + \sqrt{6}}{9}$

$\frac{16 + \sqrt{6}}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{16 + \sqrt{6}}{9}$

Decimal Form:

$2.04994330 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$