Simplify square root of (4e)/(3f)

$\sqrt{\frac{4 e}{3 f}}$

Step 1

Rewrite $\sqrt{\frac{4 e}{3 f}}$ as $\frac{\sqrt{4 e}}{\sqrt{3 f}}$ .

$\frac{\sqrt{4 e}}{\sqrt{3 f}}$

Step 2

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2} e}}{\sqrt{3 f}}$

Pull terms out from under the radical.

$\frac{2 \sqrt{e}}{\sqrt{3 f}}$

Step 3

Multiply $\frac{2 \sqrt{e}}{\sqrt{3 f}}$ by $\frac{\sqrt{3 f}}{\sqrt{3 f}}$ .

$\frac{2 \sqrt{e}}{\sqrt{3 f}} \cdot \frac{\sqrt{3 f}}{\sqrt{3 f}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{e}}{\sqrt{3 f}}$ by $\frac{\sqrt{3 f}}{\sqrt{3 f}}$ .

$\frac{2 \sqrt{e} \sqrt{3 f}}{\sqrt{3 f} \sqrt{3 f}}$

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{\sqrt{3 f}}^{1} \sqrt{3 f}}$

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{\sqrt{3 f}}^{1} {\sqrt{3 f}}^{1}}$

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{\sqrt{3 f}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{e} \sqrt{3 f}}{{\sqrt{3 f}}^{2}}$

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

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{({(3 f)}^{\frac{1}{2}})}^{2}}$

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{(3 f)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{2 \sqrt{e} \sqrt{3 f}}{{(3 f)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \sqrt{e} \sqrt{3 f}}{{(3 f)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 \sqrt{e} \sqrt{3 f}}{{(3 f)}^{1}}$

Simplify.

$\frac{2 \sqrt{e} \sqrt{3 f}}{3 f}$

Step 5

Combine using the product rule for radicals.

$\frac{2 \sqrt{3 f e}}{3 f}$