Trigonometry Examples

$\sqrt{47^{2} - {(\frac{47}{2})}^{2}}$

Step 1

Raise $47$ to the power of $2$ .

$\sqrt{2209 - {(\frac{47}{2})}^{2}}$

Step 2

Apply the product rule to $\frac{47}{2}$ .

$\sqrt{2209 - \frac{47^{2}}{2^{2}}}$

Step 3

Raise $47$ to the power of $2$ .

$\sqrt{2209 - \frac{2209}{2^{2}}}$

Step 4

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

$\sqrt{2209 - \frac{2209}{4}}$

Step 5

To write $2209$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\sqrt{2209 \cdot \frac{4}{4} - \frac{2209}{4}}$

Step 6

Combine $2209$ and $\frac{4}{4}$ .

$\sqrt{\frac{2209 \cdot 4}{4} - \frac{2209}{4}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{2209 \cdot 4 - 2209}{4}}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply $2209$ by $4$ .

$\sqrt{\frac{8836 - 2209}{4}}$

Step 8.2

Subtract $2209$ from $8836$ .

$\sqrt{\frac{6627}{4}}$

Step 9

Rewrite $\sqrt{\frac{6627}{4}}$ as $\frac{\sqrt{6627}}{\sqrt{4}}$ .

$\frac{\sqrt{6627}}{\sqrt{4}}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Rewrite $6627$ as $47^{2} \cdot 3$ .

Tap for more steps...

Step 10.1.1

Factor $2209$ out of $6627$ .

$\frac{\sqrt{2209 (3)}}{\sqrt{4}}$

Step 10.1.2

Rewrite $2209$ as $47^{2}$ .

$\frac{\sqrt{47^{2} \cdot 3}}{\sqrt{4}}$

Step 10.2

Pull terms out from under the radical.

$\frac{47 \sqrt{3}}{\sqrt{4}}$

Step 11

Simplify the denominator.

Tap for more steps...

Step 11.1

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

$\frac{47 \sqrt{3}}{\sqrt{2^{2}}}$

Step 11.2

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

$\frac{47 \sqrt{3}}{2}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{47 \sqrt{3}}{2}$

Decimal Form:

$40.70319397 \dots$