Solve for L 9.42=2(3.14) square root of L/32

$9.42 = 2 (3.14) \sqrt{\frac{L}{32}}$

Rewrite the equation as $2 (3.14) \sqrt{\frac{L}{32}} = 9.42$ .

$2 (3.14) \sqrt{\frac{L}{32}} = 9.42$

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

${(2 (3.14) \sqrt{\frac{L}{32}})}^{2} = {9.42}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{L}{32}}$ as ${(\frac{L}{32})}^{\frac{1}{2}}$ .

${(2 (3.14) {(\frac{L}{32})}^{\frac{1}{2}})}^{2} = {9.42}^{2}$

Simplify the left side.

Simplify ${(2 (3.14) {(\frac{L}{32})}^{\frac{1}{2}})}^{2}$ .

Simplify the expression.

Multiply $2$ by $3.14$ .

${(6.28 {(\frac{L}{32})}^{\frac{1}{2}})}^{2} = {9.42}^{2}$

Apply the product rule to $\frac{L}{32}$ .

${(6.28 \frac{L^{\frac{1}{2}}}{32^{\frac{1}{2}}})}^{2} = {9.42}^{2}$

Combine $6.28$ and $\frac{L^{\frac{1}{2}}}{32^{\frac{1}{2}}}$ .

${(\frac{6.28 L^{\frac{1}{2}}}{32^{\frac{1}{2}}})}^{2} = {9.42}^{2}$

Factor $6.28$ out of $6.28 L^{\frac{1}{2}}$ .

${(\frac{6.28 (L^{\frac{1}{2}})}{32^{\frac{1}{2}}})}^{2} = {9.42}^{2}$

Multiply by $1$ .

${(\frac{6.28 (L^{\frac{1}{2}})}{32^{\frac{1}{2}} \cdot 1})}^{2} = {9.42}^{2}$

Separate fractions.

${(\frac{6.28}{32^{\frac{1}{2}}} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = {9.42}^{2}$

Divide $1$ by $2$ .

${(\frac{6.28}{32^{0.5}} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = {9.42}^{2}$

Raise $32$ to the power of $0.5$ .

${(\frac{6.28}{5.65685424} \cdot \frac{L^{\frac{1}{2}}}{1})}^{2} = {9.42}^{2}$

Divide $6.28$ by $5.65685424$ .

${(1.11015764 \frac{L^{\frac{1}{2}}}{1})}^{2} = {9.42}^{2}$

Divide $L^{\frac{1}{2}}$ by $1$ .

${(1.11015764 L^{\frac{1}{2}})}^{2} = {9.42}^{2}$

Apply the product rule to $1.11015764 L^{\frac{1}{2}}$ .

${1.11015764}^{2} {(L^{\frac{1}{2}})}^{2} = {9.42}^{2}$

Raise $1.11015764$ to the power of $2$ .

$1.23245 {(L^{\frac{1}{2}})}^{2} = {9.42}^{2}$

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

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

$1.23245 L^{\frac{1}{2} \cdot 2} = {9.42}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1.23245 L^{\frac{1}{2} \cdot 2} = {9.42}^{2}$

Rewrite the expression.

$1.23245 L^{1} = {9.42}^{2}$

Simplify.

$1.23245 L = {9.42}^{2}$

Simplify the right side.

Raise $9.42$ to the power of $2$ .

$1.23245 L = 88.7364$

Divide each term in $1.23245 L = 88.7364$ by $1.23245$ and simplify.

Divide each term in $1.23245 L = 88.7364$ by $1.23245$ .

$\frac{1.23245 L}{1.23245} = \frac{88.7364}{1.23245}$

Simplify the left side.

Cancel the common factor of $1.23245$ .

Cancel the common factor.

$\frac{1.23245 L}{1.23245} = \frac{88.7364}{1.23245}$

Divide $L$ by $1$ .

$L = \frac{88.7364}{1.23245}$

Simplify the right side.

Divide $88.7364$ by $1.23245$ .

$L = 72$

Solve for L 9.42=2(3.14) square root of L/32

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