Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$\frac{x \sqrt{9 (2) x^{3}}}{3}$

Step 1.1.2

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

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

Step 1.1.3

Factor out $x^{2}$ .

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

Step 1.1.4

Move $2$ .

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

Step 1.1.5

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

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

Step 1.1.6

Add parentheses.

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Combine exponents.

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

Add $1$ and $1$ .

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

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

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $x^{2} \sqrt{2 x}$ by $1$ .

$x^{2} \sqrt{2 x}$

$x^{2} \sqrt{2 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$