Solve for L 4.5=4 square root of L/5.7

$4.5 = 4 \sqrt{\frac{L}{5.7}}$

Step 1

Rewrite the equation as $4 \sqrt{\frac{L}{5.7}} = 4.5$ .

$4 \sqrt{\frac{L}{5.7}} = 4.5$

Step 2

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

${(4 \sqrt{\frac{L}{5.7}})}^{2} = {4.5}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{L}{5.7}}$ as ${(\frac{L}{5.7})}^{\frac{1}{2}}$ .

${(4 {(\frac{L}{5.7})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the left side.

Simplify ${(4 {(\frac{L}{5.7})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(4 {(\frac{1 L}{5.7})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Factor $5.7$ out of $5.7$ .

${(4 {(\frac{1 L}{5.7 (1)})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Separate fractions.

${(4 {(\frac{1}{5.7} \cdot \frac{L}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Simplify the expression.

Divide $1$ by $5.7$ .

${(4 {(0.17543859 \frac{L}{1})}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Divide $L$ by $1$ .

${(4 {(0.17543859 L)}^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $0.17543859 L$ .

${(4 ({0.17543859}^{\frac{1}{2}} L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite $0.17543859$ as ${0.4188539}^{2}$ .

${(4 ({({0.4188539}^{2})}^{\frac{1}{2}} L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

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

${(4 ({0.4188539}^{2 (\frac{1}{2})} L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 ({0.4188539}^{2 (\frac{1}{2})} L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Rewrite the expression.

${(4 ({0.4188539}^{1} L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Evaluate the exponent.

${(4 (0.4188539 L^{\frac{1}{2}}))}^{2} = {4.5}^{2}$

Multiply $0.4188539$ by $4$ .

${(1.67541563 L^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Apply the product rule to $1.67541563 L^{\frac{1}{2}}$ .

${1.67541563}^{2} {(L^{\frac{1}{2}})}^{2} = {4.5}^{2}$

Raise $1.67541563$ to the power of $2$ .

$2.80701754 {(L^{\frac{1}{2}})}^{2} = {4.5}^{2}$

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

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

$2.80701754 L^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2.80701754 L^{\frac{1}{2} \cdot 2} = {4.5}^{2}$

Rewrite the expression.

$2.80701754 L^{1} = {4.5}^{2}$

Simplify.

$2.80701754 L = {4.5}^{2}$

Simplify the right side.

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

$2.80701754 L = 20.25$

Step 4

Divide each term in $2.80701754 L = 20.25$ by $2.80701754$ and simplify.

Divide each term in $2.80701754 L = 20.25$ by $2.80701754$ .

$\frac{2.80701754 L}{2.80701754} = \frac{20.25}{2.80701754}$

Simplify the left side.

Cancel the common factor of $2.80701754$ .

Cancel the common factor.

$\frac{2.80701754 L}{2.80701754} = \frac{20.25}{2.80701754}$

Divide $L$ by $1$ .

$L = \frac{20.25}{2.80701754}$

Simplify the right side.

Divide $20.25$ by $2.80701754$ .

$L = 7.2140625$

Solve for L 4.5=4 square root of L/5.7

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