Precalculus Examples

$\frac{x \sqrt{18 x^{3}}}{4 \sqrt{6 x}}$

Step 1

Combine $\sqrt{18 x^{3}}$ and $\sqrt{6 x}$ into a single radical.

$\frac{x \sqrt{\frac{18 x^{3}}{6 x}}}{4}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $18$ and $6$ .

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Step 2.1.1

Factor $6$ out of $18 x^{3}$ .

$\frac{x \sqrt{\frac{6 (3 x^{3})}{6 x}}}{4}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $6$ out of $6 x$ .

$\frac{x \sqrt{\frac{6 (3 x^{3})}{6 (x)}}}{4}$

Step 2.1.2.2

Cancel the common factor.

$\frac{x \sqrt{\frac{6 (3 x^{3})}{6 x}}}{4}$

Step 2.1.2.3

Rewrite the expression.

$\frac{x \sqrt{\frac{3 x^{3}}{x}}}{4}$

Step 2.2

Cancel the common factor of $x^{3}$ and $x$ .

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Step 2.2.1

Factor $x$ out of $3 x^{3}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Raise $x$ to the power of $1$ .

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

Step 2.2.2.2

Factor $x$ out of $x^{1}$ .

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

Step 2.2.2.3

Cancel the common factor.

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

Step 2.2.2.4

Rewrite the expression.

$\frac{x \sqrt{\frac{3 x^{2}}{1}}}{4}$

Step 2.2.2.5

Divide $3 x^{2}$ by $1$ .

$\frac{x \sqrt{3 x^{2}}}{4}$

Step 3

Simplify the numerator.

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Step 3.1

Reorder $3$ and $x^{2}$ .

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

Step 3.2

Pull terms out from under the radical.

$\frac{x \cdot x \sqrt{3}}{4}$

Step 3.3

Combine exponents.

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Step 3.3.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} x \sqrt{3}}{4}$

Step 3.3.2

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1} \sqrt{3}}{4}$

Step 3.3.3

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

$\frac{x^{1 + 1} \sqrt{3}}{4}$

Step 3.3.4

Add $1$ and $1$ .

$\frac{x^{2} \sqrt{3}}{4}$