Simplify (x^2)/( square root of 12x^3)

$\frac{x^{2}}{\sqrt{12 x^{3}}}$

Step 1

Simplify the denominator.

Rewrite $12 x^{3}$ as ${(2 x)}^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

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

Rewrite $4$ as $2^{2}$ .

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

Factor out $x^{2}$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $x^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $2 x \sqrt{3 x}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Simplify terms.

Combine and simplify the denominator.

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

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

Move $\sqrt{3 x}$ .

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

Raise $\sqrt{3 x}$ to the power of $1$ .

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

Raise $\sqrt{3 x}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Multiply $2$ by $3$ .

$\frac{\sqrt{3 x}}{6}$

Simplify (x^2)/( square root of 12x^3)

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