Trigonometry Examples

$\frac{10 (\sqrt{24})}{2 \sqrt{2}}$

Step 1

Cancel the common factor of $10$ and $2$ .

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Step 1.1

Factor $2$ out of $10 (\sqrt{24})$ .

$\frac{2 (5 \sqrt{24})}{2 \sqrt{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

$\frac{2 (5 \sqrt{24})}{2 (\sqrt{2})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (5 \sqrt{24})}{2 \sqrt{2}}$

Step 1.2.3

Rewrite the expression.

$\frac{5 \sqrt{24}}{\sqrt{2}}$

$\frac{5 \sqrt{24}}{\sqrt{2}}$

$\frac{5 \sqrt{24}}{\sqrt{2}}$

Step 2

Combine $\sqrt{24}$ and $\sqrt{2}$ into a single radical.

$5 \sqrt{\frac{24}{2}}$

Step 3

Divide $24$ by $2$ .

$5 \sqrt{12}$

Step 4

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 4.1

Factor $4$ out of $12$ .

$5 \sqrt{4 (3)}$

Step 4.2

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

$5 \sqrt{2^{2} \cdot 3}$

$5 \sqrt{2^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$5 (2 \sqrt{3})$

Step 6

Multiply $2$ by $5$ .

$10 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{3}$

Decimal Form:

$17.32050807 \dots$

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