Simplify square root of 6/(7x)

$\sqrt{\frac{6}{7 x}}$

Step 1

Rewrite $\sqrt{\frac{6}{7 x}}$ as $\frac{\sqrt{6}}{\sqrt{7 x}}$ .

$\frac{\sqrt{6}}{\sqrt{7 x}}$

Step 2

Multiply $\frac{\sqrt{6}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{\sqrt{6}}{\sqrt{7 x}} \cdot \frac{\sqrt{7 x}}{\sqrt{7 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{6}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$\frac{\sqrt{6} \sqrt{7 x}}{\sqrt{7 x} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{\sqrt{6} \sqrt{7 x}}{{\sqrt{7 x}}^{1} \sqrt{7 x}}$

Raise $\sqrt{7 x}$ to the power of $1$ .

$\frac{\sqrt{6} \sqrt{7 x}}{{\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1}}$

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

$\frac{\sqrt{6} \sqrt{7 x}}{{\sqrt{7 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{6} \sqrt{7 x}}{{\sqrt{7 x}}^{2}}$

Rewrite ${\sqrt{7 x}}^{2}$ as $7 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

$\frac{\sqrt{6} \sqrt{7 x}}{{({(7 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{6} \sqrt{7 x}}{{(7 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{6} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{6} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{6} \sqrt{7 x}}{{(7 x)}^{1}}$

Simplify.

$\frac{\sqrt{6} \sqrt{7 x}}{7 x}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{6 (7 x)}}{7 x}$

Multiply $6$ by $7$ .

$\frac{\sqrt{42 x}}{7 x}$