Solve for l r = square root of 3l

$r = \sqrt{3 l}$

Step 1

Rewrite the equation as $\sqrt{3 l} = r$ .

$\sqrt{3 l} = r$

Step 2

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

${\sqrt{3 l}}^{2} = r^{2}$

Step 3

Simplify each side of the equation.

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

${({(3 l)}^{\frac{1}{2}})}^{2} = r^{2}$

Simplify the left side.

Simplify ${({(3 l)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 l)}^{\frac{1}{2}})}^{2}$ .

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

${(3 l)}^{\frac{1}{2} \cdot 2} = r^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 l)}^{\frac{1}{2} \cdot 2} = r^{2}$

Rewrite the expression.

${(3 l)}^{1} = r^{2}$

Simplify.

$3 l = r^{2}$

Step 4

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

Divide each term in $3 l = r^{2}$ by $3$ .

$\frac{3 l}{3} = \frac{r^{2}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 l}{3} = \frac{r^{2}}{3}$

Divide $l$ by $1$ .

$l = \frac{r^{2}}{3}$