Solve for l 4.5=4 square root of l/5.5

$4.5 = 4 \sqrt{\frac{l}{5.5}}$

Step 1

Rewrite the equation as $4 \sqrt{\frac{l}{5.5}} = 4.5$ .

$4 \sqrt{\frac{l}{5.5}} = 4.5$

Step 2

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

${(4 \sqrt{\frac{l}{5.5}})}^{2} = {4.5}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{5.5}}$ as ${(\frac{l}{5.5})}^{\frac{1}{2}}$ .

${(4 {(\frac{l}{5.5})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the left side.

Simplify ${(4 {(\frac{l}{5.5})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(4 {(\frac{1 l}{5.5})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Factor $5.5$ out of $5.5$ .

${(4 {(\frac{1 l}{5.5 (1)})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Separate fractions.

${(4 {(\frac{1}{5.5} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the expression.

Divide $1$ by $5.5$ .

${(4 {(0.\overline{18} \frac{l}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Divide $l$ by $1$ .

${(4 {(0.\overline{18} l)}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $0.\overline{18} l$ .

${(4 ({0.\overline{18}}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite $0.\overline{18}$ as ${0.42640143}^{2}$ .

${(4 ({({0.42640143}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

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

${(4 ({0.42640143}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 ({0.42640143}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite the expression.

${(4 ({0.42640143}^{1} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Evaluate the exponent.

${(4 (0.42640143 l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Multiply $0.42640143$ by $4$ .

${(1.70560573 l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $1.70560573 l^{\frac{1}{2}}$ .

${1.70560573}^{2} {(l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Raise $1.70560573$ to the power of $2$ .

$2.\overline{90} {(l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

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

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

$2.\overline{90} l^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2.\overline{90} l^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Rewrite the expression.

$2.\overline{90} l^{1} = {4.5}^{2}$

Simplify.

$2.\overline{90} l = {4.5}^{2}$

Simplify the right side.

Raise $4.5$ to the power of $2$ .

$2.\overline{90} l = 20.25$

Step 4

Divide each term in $2.\overline{90} l = 20.25$ by $2.\overline{90}$ and simplify.

Divide each term in $2.\overline{90} l = 20.25$ by $2.\overline{90}$ .

$\frac{2.\overline{90} l}{2.\overline{90}} = \frac{20.25}{2.\overline{90}}$

Simplify the left side.

Cancel the common factor of $2.\overline{90}$ .

Cancel the common factor.

$\frac{2.\overline{90} l}{2.\overline{90}} = \frac{20.25}{2.\overline{90}}$

Divide $l$ by $1$ .

$l = \frac{20.25}{2.\overline{90}}$

Simplify the right side.

Divide $20.25$ by $2.\overline{90}$ .

$l = 6.9609375$

Solve for l 4.5=4 square root of l/5.5

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