Trigonometry Examples

$r = 12 (\sqrt[6]{\frac{102}{100} - 1})$

Step 1

Multiply $12$ by $\sqrt[6]{\frac{102}{100} - 1}$ .

$r = 12 \sqrt[6]{\frac{102}{100} - 1}$

Step 2

Simplify $12 \sqrt[6]{\frac{102}{100} - 1}$ .

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Step 2.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$r = 12 \sqrt[6]{\frac{102}{100} - 1 \cdot \frac{100}{100}}$

Step 2.2

Combine $- 1$ and $\frac{100}{100}$ .

$r = 12 \sqrt[6]{\frac{102}{100} + \frac{- 1 \cdot 100}{100}}$

Step 2.3

Combine the numerators over the common denominator.

$r = 12 \sqrt[6]{\frac{102 - 1 \cdot 100}{100}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 1$ by $100$ .

$r = 12 \sqrt[6]{\frac{102 - 100}{100}}$

Step 2.4.2

Subtract $100$ from $102$ .

$r = 12 \sqrt[6]{\frac{2}{100}}$

Step 2.5

Cancel the common factor of $2$ and $100$ .

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Step 2.5.1

Factor $2$ out of $2$ .

$r = 12 \sqrt[6]{\frac{2 (1)}{100}}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $100$ .

$r = 12 \sqrt[6]{\frac{2 \cdot 1}{2 \cdot 50}}$

Step 2.5.2.2

Cancel the common factor.

$r = 12 \sqrt[6]{\frac{2 \cdot 1}{2 \cdot 50}}$

Step 2.5.2.3

Rewrite the expression.

$r = 12 \sqrt[6]{\frac{1}{50}}$

Step 2.6

Rewrite $\sqrt[6]{\frac{1}{50}}$ as $\frac{\sqrt[6]{1}}{\sqrt[6]{50}}$ .

$r = 12 \frac{\sqrt[6]{1}}{\sqrt[6]{50}}$

Step 2.7

Any root of $1$ is $1$ .

$r = 12 \frac{1}{\sqrt[6]{50}}$

Step 2.8

Combine $12$ and $\frac{1}{\sqrt[6]{50}}$ .

$r = \frac{12}{\sqrt[6]{50}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = \frac{12}{\sqrt[6]{50}}$

Decimal Form:

$r = 6.25200877 \dots$