Simplify the Radical Expression square root of 2/(7b)

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

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

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

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $2$ by $7$ .

$\frac{\sqrt{14 b}}{7 b}$