Trigonometry Examples

$20 \sqrt{3} (\frac{\sqrt{3}}{2})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $20 \sqrt{3}$ .

$2 (10 \sqrt{3}) \frac{\sqrt{3}}{2}$

Step 1.2

Cancel the common factor.

$2 (10 \sqrt{3}) \frac{\sqrt{3}}{2}$

Step 1.3

Rewrite the expression.

$10 \sqrt{3} \sqrt{3}$

Step 2

Raise $\sqrt{3}$ to the power of $1$ .

$10 ({\sqrt{3}}^{1} \sqrt{3})$

Step 3

Raise $\sqrt{3}$ to the power of $1$ .

$10 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 4

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

$10 {\sqrt{3}}^{1 + 1}$

Step 5

Add $1$ and $1$ .

$10 {\sqrt{3}}^{2}$

Step 6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$10 {(3^{\frac{1}{2}})}^{2}$

Step 6.2

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

$10 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$10 \cdot 3^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$10 \cdot 3^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$10 \cdot 3^{1}$

Step 6.5

Evaluate the exponent.

$10 \cdot 3$

Step 7

Multiply $10$ by $3$ .

$30$