Solve for f r = square root of (kq^1q^2)/f

$r = \sqrt{\frac{k q^{1} q^{2}}{f}}$

Rewrite the equation as $\sqrt{\frac{k q^{1} q^{2}}{f}} = r$ .

$\sqrt{\frac{k q \cdot q^{2}}{f}} = r$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{k q^{1} q^{2}}{f}}}^{2} = r^{2}$

Simplify each side of the equation.

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

${({(\frac{k q^{1} q^{2}}{f})}^{\frac{1}{2}})}^{2} = r^{2}$

Simplify the left side.

Simplify ${({(\frac{k q^{1} q^{2}}{f})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{k q^{1} q^{2}}{f})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{k q^{1} q^{2}}{f})}^{\frac{1}{2} \cdot 2} = r^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{k q^{1} q^{2}}{f})}^{\frac{1}{2} \cdot 2} = r^{2}$

Rewrite the expression.

${(\frac{k q^{1} q^{2}}{f})}^{1} = r^{2}$

Multiply $q^{1}$ by $q^{2}$ by adding the exponents.

Move $q^{2}$ .

${(\frac{k (q^{2} q^{1})}{f})}^{1} = r^{2}$

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

${(\frac{k q^{2 + 1}}{f})}^{1} = r^{2}$

Add $2$ and $1$ .

${(\frac{k q^{3}}{f})}^{1} = r^{2}$

Simplify.

$\frac{k q^{3}}{f} = r^{2}$

Solve for $f$ .

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$f, 1$

The LCM of one and any expression is the expression.

$f$

Multiply each term in $\frac{k q^{3}}{f} = r^{2}$ by $f$ to eliminate the fractions.

Multiply each term in $\frac{k q^{3}}{f} = r^{2}$ by $f$ .

$\frac{k q^{3}}{f} f = r^{2} f$

Simplify the left side.

Cancel the common factor of $f$ .

Cancel the common factor.

$\frac{k q^{3}}{f} f = r^{2} f$

Rewrite the expression.

$k q^{3} = r^{2} f$

Solve the equation.

Rewrite the equation as $r^{2} f = k q^{3}$ .

$r^{2} f = k q^{3}$

Divide each term in $r^{2} f = k q^{3}$ by $r^{2}$ and simplify.

Divide each term in $r^{2} f = k q^{3}$ by $r^{2}$ .

$\frac{r^{2} f}{r^{2}} = \frac{k q^{3}}{r^{2}}$

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{r^{2} f}{r^{2}} = \frac{k q^{3}}{r^{2}}$

Divide $f$ by $1$ .

$f = \frac{k q^{3}}{r^{2}}$

Solve for f r = square root of (kq^1q^2)/f

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