Trigonometry Examples

$\sqrt{16^{2} - 32^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Raise $16$ to the power of $2$ .

$\sqrt{256 - 32^{2}}$

Step 1.2

Raise $32$ to the power of $2$ .

$\sqrt{256 - 1 \cdot 1024}$

Step 1.3

Multiply $- 1$ by $1024$ .

$\sqrt{256 - 1024}$

Step 1.4

Subtract $1024$ from $256$ .

$\sqrt{- 768}$

$\sqrt{- 768}$

Step 2

Rewrite $- 768$ as $- 1 (768)$ .

$\sqrt{- 1 (768)}$

Step 3

Rewrite $\sqrt{- 1 (768)}$ as $\sqrt{- 1} \cdot \sqrt{768}$ .

$\sqrt{- 1} \cdot \sqrt{768}$

Step 4

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{768}$

Step 5

Rewrite $768$ as $16^{2} \cdot 3$ .

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Step 5.1

Factor $256$ out of $768$ .

$i \cdot \sqrt{256 (3)}$

Step 5.2

Rewrite $256$ as $16^{2}$ .

$i \cdot \sqrt{16^{2} \cdot 3}$

$i \cdot \sqrt{16^{2} \cdot 3}$

Step 6

Pull terms out from under the radical.

$i \cdot (16 \sqrt{3})$

Step 7

Move $16$ to the left of $i$ .

$16 i \sqrt{3}$

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