Simplify square root of 7/(2x)

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

Step 1

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

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

Step 2

Multiply $\frac{\sqrt{7}}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{7}}{\sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7}}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

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

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1} \sqrt{2 x}}$

Raise $\sqrt{2 x}$ to the power of $1$ .

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}}$

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

$\frac{\sqrt{7} \sqrt{2 x}}{{\sqrt{2 x}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $7$ by $2$ .

$\frac{\sqrt{14 x}}{2 x}$