Trigonometry Examples

$\frac{- 8 + \sqrt{28}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 1.1.1

Factor $4$ out of $28$ .

$\frac{- 8 + \sqrt{4 (7)}}{2}$

Step 1.1.2

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

$\frac{- 8 + \sqrt{2^{2} \cdot 7}}{2}$

$\frac{- 8 + \sqrt{2^{2} \cdot 7}}{2}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 8 + 2 \sqrt{7}}{2}$

$\frac{- 8 + 2 \sqrt{7}}{2}$

Step 2

Cancel the common factor of $- 8 + 2 \sqrt{7}$ and $2$ .

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Step 2.1

Factor $2$ out of $- 8$ .

$\frac{2 \cdot - 4 + 2 \sqrt{7}}{2}$

Step 2.2

Factor $2$ out of $2 \sqrt{7}$ .

$\frac{2 \cdot - 4 + 2 (\sqrt{7})}{2}$

Step 2.3

Factor $2$ out of $2 (- 4) + 2 (\sqrt{7})$ .

$\frac{2 (- 4 + \sqrt{7})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 4 + \sqrt{7})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (- 4 + \sqrt{7})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{- 4 + \sqrt{7}}{1}$

Step 2.4.4

Divide $- 4 + \sqrt{7}$ by $1$ .

$- 4 + \sqrt{7}$

$- 4 + \sqrt{7}$

$- 4 + \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 4 + \sqrt{7}$

Decimal Form:

$- 1.35424868 \dots$

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