Trigonometry Examples

$\sqrt{{(\frac{8}{3})}^{2} + {(5)}^{2}}$

Step 1

Apply the product rule to $\frac{8}{3}$ .

$\sqrt{\frac{8^{2}}{3^{2}} + {(5)}^{2}}$

Step 2

Raise $8$ to the power of $2$ .

$\sqrt{\frac{64}{3^{2}} + {(5)}^{2}}$

Step 3

Raise $3$ to the power of $2$ .

$\sqrt{\frac{64}{9} + {(5)}^{2}}$

Step 4

Raise $5$ to the power of $2$ .

$\sqrt{\frac{64}{9} + 25}$

Step 5

To write $25$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\sqrt{\frac{64}{9} + 25 \cdot \frac{9}{9}}$

Step 6

Combine $25$ and $\frac{9}{9}$ .

$\sqrt{\frac{64}{9} + \frac{25 \cdot 9}{9}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{64 + 25 \cdot 9}{9}}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $25$ by $9$ .

$\sqrt{\frac{64 + 225}{9}}$

Step 8.2

Add $64$ and $225$ .

$\sqrt{\frac{289}{9}}$

Step 9

Rewrite $\sqrt{\frac{289}{9}}$ as $\frac{\sqrt{289}}{\sqrt{9}}$ .

$\frac{\sqrt{289}}{\sqrt{9}}$

Step 10

Simplify the numerator.

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Step 10.1

Rewrite $289$ as $17^{2}$ .

$\frac{\sqrt{17^{2}}}{\sqrt{9}}$

Step 10.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{17}{\sqrt{9}}$

Step 11

Simplify the denominator.

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Step 11.1

Rewrite $9$ as $3^{2}$ .

$\frac{17}{\sqrt{3^{2}}}$

Step 11.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{17}{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{3}$

Decimal Form:

$5.\overline{6}$

Mixed Number Form:

$5 \frac{2}{3}$