Simplify the Radical Expression square root of 7/(3z)

$\sqrt{\frac{7}{3 z}}$

Rewrite $\sqrt{\frac{7}{3 z}}$ as $\frac{\sqrt{7}}{\sqrt{3 z}}$ .

$\frac{\sqrt{7}}{\sqrt{3 z}}$

Multiply $\frac{\sqrt{7}}{\sqrt{3 z}}$ by $\frac{\sqrt{3 z}}{\sqrt{3 z}}$ .

$\frac{\sqrt{7}}{\sqrt{3 z}} \cdot \frac{\sqrt{3 z}}{\sqrt{3 z}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7}}{\sqrt{3 z}}$ by $\frac{\sqrt{3 z}}{\sqrt{3 z}}$ .

$\frac{\sqrt{7} \sqrt{3 z}}{\sqrt{3 z} \sqrt{3 z}}$

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

$\frac{\sqrt{7} \sqrt{3 z}}{{\sqrt{3 z}}^{1} \sqrt{3 z}}$

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

$\frac{\sqrt{7} \sqrt{3 z}}{{\sqrt{3 z}}^{1} {\sqrt{3 z}}^{1}}$

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

$\frac{\sqrt{7} \sqrt{3 z}}{{\sqrt{3 z}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{7} \sqrt{3 z}}{{\sqrt{3 z}}^{2}}$

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

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

$\frac{\sqrt{7} \sqrt{3 z}}{{({(3 z)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{7} \sqrt{3 z}}{{(3 z)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{7} \sqrt{3 z}}{{(3 z)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{7} \sqrt{3 z}}{{(3 z)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{7} \sqrt{3 z}}{{(3 z)}^{1}}$

Simplify.

$\frac{\sqrt{7} \sqrt{3 z}}{3 z}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{7 (3 z)}}{3 z}$

Multiply $7$ by $3$ .

$\frac{\sqrt{21 z}}{3 z}$