Trigonometry Examples

\frac{5 \sqrt{28}}{28}

$\frac{5 \sqrt{28}}{28}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

28

$28$ as

2^{2} \cdot 7

$2^{2} \cdot 7$ .

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Step 1.1.1

Factor

4

$4$ out of

28

$28$ .

\frac{5 \sqrt{4 (7)}}{28}

$\frac{5 \sqrt{4 (7)}}{28}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\frac{5 \sqrt{2^{2} \cdot 7}}{28}

$\frac{5 \sqrt{2^{2} \cdot 7}}{28}$

\frac{5 \sqrt{2^{2} \cdot 7}}{28}

$\frac{5 \sqrt{2^{2} \cdot 7}}{28}$

Step 1.2

Pull terms out from under the radical.

\frac{5 \cdot 2 \sqrt{7}}{28}

$\frac{5 \cdot 2 \sqrt{7}}{28}$

Step 1.3

Multiply

5

$5$ by

2

$2$ .

\frac{10 \sqrt{7}}{28}

$\frac{10 \sqrt{7}}{28}$

\frac{10 \sqrt{7}}{28}

$\frac{10 \sqrt{7}}{28}$

Step 2

Cancel the common factor of

10

$10$ and

28

$28$ .

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Step 2.1

Factor

2

$2$ out of

10 \sqrt{7}

$10 \sqrt{7}$ .

\frac{2 (5 \sqrt{7})}{28}

$\frac{2 (5 \sqrt{7})}{28}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

2

$2$ out of

28

$28$ .

\frac{2 (5 \sqrt{7})}{2 (14)}

$\frac{2 (5 \sqrt{7})}{2 (14)}$

Step 2.2.2

Cancel the common factor.

\frac{2 (5 \sqrt{7})}{2 \cdot 14}

$\frac{2 (5 \sqrt{7})}{2 \cdot 14}$

Step 2.2.3

Rewrite the expression.

\frac{5 \sqrt{7}}{14}

$\frac{5 \sqrt{7}}{14}$

\frac{5 \sqrt{7}}{14}

$\frac{5 \sqrt{7}}{14}$

\frac{5 \sqrt{7}}{14}

$\frac{5 \sqrt{7}}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{5 \sqrt{7}}{14}

$\frac{5 \sqrt{7}}{14}$

Decimal Form:

0.94491118 \dots

$0.94491118 \dots$

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

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