Trigonometry Examples

$\sqrt{\frac{1}{2} \cdot (1 - \frac{8}{17})}$

Step 1

Simplify the expression.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{1}{2} (\frac{17}{17} - \frac{8}{17})}$

Step 1.2

Combine the numerators over the common denominator.

$\sqrt{\frac{1}{2} \cdot \frac{17 - 8}{17}}$

Step 1.3

Subtract $8$ from $17$ .

$\sqrt{\frac{1}{2} \cdot \frac{9}{17}}$

Step 2

Multiply $\frac{1}{2}$ by $\frac{9}{17}$ .

$\sqrt{\frac{9}{2 \cdot 17}}$

Step 3

Multiply $2$ by $17$ .

$\sqrt{\frac{9}{34}}$

Step 4

Rewrite $\sqrt{\frac{9}{34}}$ as $\frac{\sqrt{9}}{\sqrt{34}}$ .

$\frac{\sqrt{9}}{\sqrt{34}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{\sqrt{34}}$

Step 5.2

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

$\frac{3}{\sqrt{34}}$

Step 6

Multiply $\frac{3}{\sqrt{34}}$ by $\frac{\sqrt{34}}{\sqrt{34}}$ .

$\frac{3}{\sqrt{34}} \cdot \frac{\sqrt{34}}{\sqrt{34}}$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{3}{\sqrt{34}}$ by $\frac{\sqrt{34}}{\sqrt{34}}$ .

$\frac{3 \sqrt{34}}{\sqrt{34} \sqrt{34}}$

Step 7.2

Raise $\sqrt{34}$ to the power of $1$ .

$\frac{3 \sqrt{34}}{{\sqrt{34}}^{1} \sqrt{34}}$

Step 7.3

Raise $\sqrt{34}$ to the power of $1$ .

$\frac{3 \sqrt{34}}{{\sqrt{34}}^{1} {\sqrt{34}}^{1}}$

Step 7.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \sqrt{34}}{{\sqrt{34}}^{1 + 1}}$

Step 7.5

Add $1$ and $1$ .

$\frac{3 \sqrt{34}}{{\sqrt{34}}^{2}}$

Step 7.6

Rewrite ${\sqrt{34}}^{2}$ as $34$ .

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{34}$ as $34^{\frac{1}{2}}$ .

$\frac{3 \sqrt{34}}{{(34^{\frac{1}{2}})}^{2}}$

Step 7.6.2

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

$\frac{3 \sqrt{34}}{34^{\frac{1}{2} \cdot 2}}$

Step 7.6.3

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

$\frac{3 \sqrt{34}}{34^{\frac{2}{2}}}$

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

$\frac{3 \sqrt{34}}{34^{\frac{2}{2}}}$

Step 7.6.4.2

Rewrite the expression.

$\frac{3 \sqrt{34}}{34^{1}}$

Step 7.6.5

Evaluate the exponent.

$\frac{3 \sqrt{34}}{34}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{34}}{34}$

Decimal Form:

$0.51449575 \dots$