Trigonometry Examples

v ((17^{2}) - ({(4 \sqrt{17})}^{2}))

$v ((17^{2}) - ({(4 \sqrt{17})}^{2}))$

Step 1

Simplify each term.

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Step 1.1

Raise

17

$17$ to the power of

2

$2$ .

v (289 - ({(4 \sqrt{17})}^{2}))

$v (289 - ({(4 \sqrt{17})}^{2}))$

Step 1.2

Apply the product rule to

4 \sqrt{17}

$4 \sqrt{17}$ .

v (289 - (4^{2} {\sqrt{17}}^{2}))

$v (289 - (4^{2} {\sqrt{17}}^{2}))$

Step 1.3

Raise

4

$4$ to the power of

2

$2$ .

v (289 - (16 {\sqrt{17}}^{2}))

$v (289 - (16 {\sqrt{17}}^{2}))$

Step 1.4

Rewrite

{\sqrt{17}}^{2}

${\sqrt{17}}^{2}$ as

17

$17$ .

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Step 1.4.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{17}

$\sqrt{17}$ as

17^{\frac{1}{2}}

$17^{\frac{1}{2}}$ .

v (289 - (16 {(17^{\frac{1}{2}})}^{2}))

$v (289 - (16 {(17^{\frac{1}{2}})}^{2}))$

Step 1.4.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

$v (289 - (16 \cdot 17^{\frac{1}{2} \cdot 2}))$

Step 1.4.3

Combine

$\frac{1}{2}$ and

$2$ .

$v (289 - (16 \cdot 17^{\frac{2}{2}}))$

Step 1.4.4

Cancel the common factor of

$2$ .

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Step 1.4.4.1

Cancel the common factor.

$v (289 - (16 \cdot 17^{\frac{2}{2}}))$

Step 1.4.4.2

Rewrite the expression.

$v (289 - (16 \cdot 17^{1}))$

$v (289 - (16 \cdot 17^{1}))$

Step 1.4.5

Evaluate the exponent.

$v (289 - (16 \cdot 17))$

$v (289 - (16 \cdot 17))$

Step 1.5

Multiply

$- (16 \cdot 17)$ .

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Step 1.5.1

Multiply

$16$ by

$17$ .

$v (289 - 1 \cdot 272)$

Step 1.5.2

Multiply

$- 1$ by

$272$ .

$v (289 - 272)$

$v (289 - 272)$

$v (289 - 272)$

Step 2

Simplify the expression.

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Step 2.1

Subtract

$272$ from

$289$ .

$v \cdot 17$

Step 2.2

Move

$17$ to the left of

$v$ .

$17 v$

$17 v$

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