Trigonometry Examples

$4 {(\sqrt{3})}^{2}$

Step 1

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

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Step 1.1

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

$4 {(3^{\frac{1}{2}})}^{2}$

Step 1.2

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

$4 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 1.3

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

$4 \cdot 3^{\frac{2}{2}}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$4 \cdot 3^{\frac{2}{2}}$

Step 1.4.2

Rewrite the expression.

$4 \cdot 3^{1}$

Step 1.5

Evaluate the exponent.

$4 \cdot 3$

Step 2

Multiply $4$ by $3$ .

$12$