Solve for L 2.5 = square root of L/3.7

$2.5 = \sqrt{\frac{L}{3.7}}$

Rewrite the equation as $\sqrt{\frac{L}{3.7}} = 2.5$ .

$\sqrt{\frac{L}{3.7}} = 2.5$

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

${\sqrt{\frac{L}{3.7}}}^{2} = {2.5}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{L}{3.7}}$ as ${(\frac{L}{3.7})}^{\frac{1}{2}}$ .

${({(\frac{L}{3.7})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Simplify the left side.

Simplify ${({(\frac{L}{3.7})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{L}{3.7})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{L}{3.7})}^{\frac{1}{2} \cdot 2} = {2.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{L}{3.7})}^{\frac{1}{2} \cdot 2} = {2.5}^{2}$

Rewrite the expression.

${(\frac{L}{3.7})}^{1} = {2.5}^{2}$

Multiply by $1$ .

${(\frac{1 L}{3.7})}^{1} = {2.5}^{2}$

Factor $3.7$ out of $3.7$ .

${(\frac{1 L}{3.7 (1)})}^{1} = {2.5}^{2}$

Separate fractions.

${(\frac{1}{3.7} \cdot \frac{L}{1})}^{1} = {2.5}^{2}$

Divide $1$ by $3.7$ .

${(0.\overline{270} \frac{L}{1})}^{1} = {2.5}^{2}$

Divide $L$ by $1$ .

${(0.\overline{270} L)}^{1} = {2.5}^{2}$

Simplify.

$0.\overline{270} L = {2.5}^{2}$

Simplify the right side.

Raise $2.5$ to the power of $2$ .

$0.\overline{270} L = 6.25$

Divide each term in $0.\overline{270} L = 6.25$ by $0.\overline{270}$ and simplify.

Divide each term in $0.\overline{270} L = 6.25$ by $0.\overline{270}$ .

$\frac{0.\overline{270} L}{0.\overline{270}} = \frac{6.25}{0.\overline{270}}$

Simplify the left side.

Cancel the common factor of $0.\overline{270}$ .

Cancel the common factor.

$\frac{0.\overline{270} L}{0.\overline{270}} = \frac{6.25}{0.\overline{270}}$

Divide $L$ by $1$ .

$L = \frac{6.25}{0.\overline{270}}$

Simplify the right side.

Divide $6.25$ by $0.\overline{270}$ .

$L = 23.124\overline{9}$