Solve for l 4.5=4 square root of l/5.9

$4.5 = 4 \sqrt{\frac{l}{5.9}}$

Step 1

Rewrite the equation as $4 \sqrt{\frac{l}{5.9}} = 4.5$ .

$4 \sqrt{\frac{l}{5.9}} = 4.5$

Step 2

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

${(4 \sqrt{\frac{l}{5.9}})}^{2} = {4.5}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{5.9}}$ as ${(\frac{l}{5.9})}^{\frac{1}{2}}$ .

${(4 {(\frac{l}{5.9})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the left side.

Simplify ${(4 {(\frac{l}{5.9})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(4 {(\frac{1 l}{5.9})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Factor $5.9$ out of $5.9$ .

${(4 {(\frac{1 l}{5.9 (1)})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Separate fractions.

${(4 {(\frac{1}{5.9} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the expression.

Divide $1$ by $5.9$ .

${(4 {(0.16949152 \frac{l}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Divide $l$ by $1$ .

${(4 {(0.16949152 l)}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $0.16949152 l$ .

${(4 ({0.16949152}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite $0.16949152$ as ${0.41169348}^{2}$ .

${(4 ({({0.41169348}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

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

${(4 ({0.41169348}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 ({0.41169348}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite the expression.

${(4 ({0.41169348}^{1} l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Evaluate the exponent.

${(4 (0.41169348 l^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Multiply $0.41169348$ by $4$ .

${(1.64677393 l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $1.64677393 l^{\frac{1}{2}}$ .

${1.64677393}^{2} {(l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Raise $1.64677393$ to the power of $2$ .

$2.7118644 {(l^{\frac{1}{2}})}^{2} = {4.5}^{2}$

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

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

$2.7118644 l^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2.7118644 l^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Rewrite the expression.

$2.7118644 l^{1} = {4.5}^{2}$

Simplify.

$2.7118644 l = {4.5}^{2}$

Simplify the right side.

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

$2.7118644 l = 20.25$

Step 4

Divide each term in $2.7118644 l = 20.25$ by $2.7118644$ and simplify.

Divide each term in $2.7118644 l = 20.25$ by $2.7118644$ .

$\frac{2.7118644 l}{2.7118644} = \frac{20.25}{2.7118644}$

Simplify the left side.

Cancel the common factor of $2.7118644$ .

Cancel the common factor.

$\frac{2.7118644 l}{2.7118644} = \frac{20.25}{2.7118644}$

Divide $l$ by $1$ .

$l = \frac{20.25}{2.7118644}$

Simplify the right side.

Divide $20.25$ by $2.7118644$ .

$l = 7.4671875$

Solve for l 4.5=4 square root of l/5.9

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