Simplify 3/( square root of 6x)

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

Step 1

Multiply $\frac{3}{\sqrt{6 x}}$ by $\frac{\sqrt{6 x}}{\sqrt{6 x}}$ .

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

Step 2

Combine and simplify the denominator.

Multiply $\frac{3}{\sqrt{6 x}}$ by $\frac{\sqrt{6 x}}{\sqrt{6 x}}$ .

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

Raise $\sqrt{6 x}$ to the power of $1$ .

$\frac{3 \sqrt{6 x}}{{\sqrt{6 x}}^{1} \sqrt{6 x}}$

Raise $\sqrt{6 x}$ to the power of $1$ .

$\frac{3 \sqrt{6 x}}{{\sqrt{6 x}}^{1} {\sqrt{6 x}}^{1}}$

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

$\frac{3 \sqrt{6 x}}{{\sqrt{6 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 \sqrt{6 x}}{{\sqrt{6 x}}^{2}}$

Rewrite ${\sqrt{6 x}}^{2}$ as $6 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x}$ as ${(6 x)}^{\frac{1}{2}}$ .

$\frac{3 \sqrt{6 x}}{{({(6 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{3 \sqrt{6 x}}{{(6 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{3 \sqrt{6 x}}{{(6 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \sqrt{6 x}}{{(6 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{3 \sqrt{6 x}}{{(6 x)}^{1}}$

Simplify.

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

Step 3

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3 \sqrt{6 x}$ .

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

Cancel the common factors.

Factor $3$ out of $6 x$ .

$\frac{3 (\sqrt{6 x})}{3 (2 x)}$

Cancel the common factor.

$\frac{3 \sqrt{6 x}}{3 (2 x)}$

Rewrite the expression.

$\frac{\sqrt{6 x}}{2 x}$