Trigonometry Examples

$r^{2} = 75$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$r = \pm \sqrt{75}$

Step 2

Simplify $\pm \sqrt{75}$ .

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Step 2.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 2.1.1

Factor $25$ out of $75$ .

$r = \pm \sqrt{25 (3)}$

Step 2.1.2

Rewrite $25$ as $5^{2}$ .

$r = \pm \sqrt{5^{2} \cdot 3}$

Step 2.2

Pull terms out from under the radical.

$r = \pm 5 \sqrt{3}$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$r = 5 \sqrt{3}$

Step 3.2

Next, use the negative value of the $\pm$ to find the second solution.

$r = - 5 \sqrt{3}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

$r = 5 \sqrt{3}, - 5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = 5 \sqrt{3}, - 5 \sqrt{3}$

Decimal Form:

$r = 8.66025403 \dots, - 8.66025403 \dots$