Trigonometry Examples

$\frac{\sqrt{11 x}}{\sqrt{15}}$

Step 1

Multiply $\frac{\sqrt{11 x}}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{\sqrt{11 x}}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{\sqrt{11 x}}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{\sqrt{11 x} \sqrt{15}}{\sqrt{15} \sqrt{15}}$

Step 2.2

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{\sqrt{11 x} \sqrt{15}}{{\sqrt{15}}^{1} \sqrt{15}}$

Step 2.3

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{\sqrt{11 x} \sqrt{15}}{{\sqrt{15}}^{1} {\sqrt{15}}^{1}}$

Step 2.4

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

$\frac{\sqrt{11 x} \sqrt{15}}{{\sqrt{15}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{\sqrt{11 x} \sqrt{15}}{{\sqrt{15}}^{2}}$

Step 2.6

Rewrite ${\sqrt{15}}^{2}$ as $15$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15}$ as $15^{\frac{1}{2}}$ .

$\frac{\sqrt{11 x} \sqrt{15}}{{(15^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$\frac{\sqrt{11 x} \sqrt{15}}{15^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$\frac{\sqrt{11 x} \sqrt{15}}{15^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{\sqrt{11 x} \sqrt{15}}{15^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{\sqrt{11 x} \sqrt{15}}{15^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{\sqrt{11 x} \sqrt{15}}{15}$

Step 3

Simplify the numerator.

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Step 3.1

Combine using the product rule for radicals.

$\frac{\sqrt{11 x \cdot 15}}{15}$

Step 3.2

Multiply $15$ by $11$ .

$\frac{\sqrt{165 x}}{15}$