Simplify square root of 18/(x^3)

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

Step 1

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

Factor the perfect power $3^{2}$ out of $18$ .

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

Factor the perfect power $x^{2}$ out of $x^{3}$ .

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

Rearrange the fraction $\frac{3^{2} \cdot 2}{x^{2} x}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $\sqrt{\frac{2}{x}}$ as $\frac{\sqrt{2}}{\sqrt{x}}$ .

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

Step 4

Multiply $\frac{\sqrt{2}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Step 5

Combine and simplify the denominator.

Multiply $\frac{\sqrt{2}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 6

Combine using the product rule for radicals.

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

Step 7

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

Multiply $\frac{3}{x}$ by $\frac{\sqrt{2 x}}{x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify square root of 18/(x^3)

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