Trigonometry Examples

$v ({(8)}^{2} + {(- \sqrt{17})}^{2})$

Step 1

Simplify each term.

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Step 1.1

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

$v (64 + {(- \sqrt{17})}^{2})$

Step 1.2

Apply the product rule to $- \sqrt{17}$ .

$v (64 + {(- 1)}^{2} {\sqrt{17}}^{2})$

Step 1.3

Raise $- 1$ to the power of $2$ .

$v (64 + 1 {\sqrt{17}}^{2})$

Step 1.4

Multiply ${\sqrt{17}}^{2}$ by $1$ .

$v (64 + {\sqrt{17}}^{2})$

Step 1.5

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

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Step 1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$v (64 + {(17^{\frac{1}{2}})}^{2})$

Step 1.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$v (64 + 17^{\frac{1}{2} \cdot 2})$

Step 1.5.3

Combine $\frac{1}{2}$ and $2$ .

$v (64 + 17^{\frac{2}{2}})$

Step 1.5.4

Cancel the common factor of $2$ .

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Step 1.5.4.1

Cancel the common factor.

$v (64 + 17^{\frac{2}{2}})$

Step 1.5.4.2

Rewrite the expression.

$v (64 + 17^{1})$

Step 1.5.5

Evaluate the exponent.

$v (64 + 17)$

Step 2

Simplify the expression.

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Step 2.1

Add $64$ and $17$ .

$v \cdot 81$

Step 2.2

Move $81$ to the left of $v$ .

$81 v$