Trigonometry Examples

$\frac{5.5}{\sqrt{18}}$

Step 1

Simplify the denominator.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$\frac{5.5}{\sqrt{9 (2)}}$

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

$\frac{5.5}{\sqrt{3^{2} \cdot 2}}$

Pull terms out from under the radical.

$\frac{5.5}{3 \sqrt{2}}$

Step 2

Multiply $\frac{5.5}{3 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{5.5}{3 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 3

Combine and simplify the denominator.

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Multiply $\frac{5.5}{3 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{5.5 \sqrt{2}}{3 \sqrt{2} \sqrt{2}}$

Move $\sqrt{2}$ .

$\frac{5.5 \sqrt{2}}{3 (\sqrt{2} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{5.5 \sqrt{2}}{3 ({\sqrt{2}}^{1} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{5.5 \sqrt{2}}{3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

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

$\frac{5.5 \sqrt{2}}{3 {\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5.5 \sqrt{2}}{3 {\sqrt{2}}^{2}}$

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

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

$\frac{5.5 \sqrt{2}}{3 {(2^{\frac{1}{2}})}^{2}}$

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

$\frac{5.5 \sqrt{2}}{3 \cdot 2^{\frac{1}{2} \cdot 2}}$

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

$\frac{5.5 \sqrt{2}}{3 \cdot 2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{5.5 \sqrt{2}}{3 \cdot 2^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5.5 \sqrt{2}}{3 \cdot 2^{1}}$

Evaluate the exponent.

$\frac{5.5 \sqrt{2}}{3 \cdot 2}$

Step 4

Multiply $5.5$ by $\sqrt{2}$ .

$\frac{7.77817459}{3 \cdot 2}$

Step 5

Simplify the expression.

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Multiply $3$ by $2$ .

$\frac{7.77817459}{6}$

Divide $7.77817459$ by $6$ .

$1.29636243$