Solve for L 3=2pi square root of L/9.8

$3 = 2 π \sqrt{\frac{L}{9.8}}$

Step 1

Rewrite the equation as $2 π \sqrt{\frac{L}{9.8}} = 3$ .

$2 π \sqrt{\frac{L}{9.8}} = 3$

Step 2

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

${(2 π \sqrt{\frac{L}{9.8}})}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{L}{9.8}}$ as ${(\frac{L}{9.8})}^{\frac{1}{2}}$ .

${(2 π {(\frac{L}{9.8})}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${(2 π {(\frac{L}{9.8})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(2 π {(\frac{1 L}{9.8})}^{\frac{1}{2}})}^{2} = 3^{2}$

Factor $9.8$ out of $9.8$ .

${(2 π {(\frac{1 L}{9.8 (1)})}^{\frac{1}{2}})}^{2} = 3^{2}$

Separate fractions.

${(2 π {(\frac{1}{9.8} \cdot \frac{L}{1})}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the expression.

Divide $1$ by $9.8$ .

${(2 π {(0.10204081 \frac{L}{1})}^{\frac{1}{2}})}^{2} = 3^{2}$

Divide $L$ by $1$ .

${(2 π {(0.10204081 L)}^{\frac{1}{2}})}^{2} = 3^{2}$

Apply the product rule to $0.10204081 L$ .

${(2 π ({0.10204081}^{\frac{1}{2}} L^{\frac{1}{2}}))}^{2} = 3^{2}$

Rewrite $0.10204081$ as ${0.31943828}^{2}$ .

${(2 π ({({0.31943828}^{2})}^{\frac{1}{2}} L^{\frac{1}{2}}))}^{2} = 3^{2}$

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

${(2 π ({0.31943828}^{2 (\frac{1}{2})} L^{\frac{1}{2}}))}^{2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 π ({0.31943828}^{2 (\frac{1}{2})} L^{\frac{1}{2}}))}^{2} = 3^{2}$

Rewrite the expression.

${(2 π ({0.31943828}^{1} L^{\frac{1}{2}}))}^{2} = 3^{2}$

Evaluate the exponent.

${(2 π (0.31943828 L^{\frac{1}{2}}))}^{2} = 3^{2}$

Multiply $2 π (0.31943828 L^{\frac{1}{2}})$ .

Multiply $0.31943828$ by $2$ .

${(0.63887656 π L^{\frac{1}{2}})}^{2} = 3^{2}$

Multiply $0.63887656$ by $π$ .

${(2.00708992 L^{\frac{1}{2}})}^{2} = 3^{2}$

Apply the product rule to $2.00708992 L^{\frac{1}{2}}$ .

${2.00708992}^{2} {(L^{\frac{1}{2}})}^{2} = 3^{2}$

Raise $2.00708992$ to the power of $2$ .

$4.02840995 {(L^{\frac{1}{2}})}^{2} = 3^{2}$

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

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

$4.02840995 L^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4.02840995 L^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

$4.02840995 L^{1} = 3^{2}$

Simplify.

$4.02840995 L = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$4.02840995 L = 9$

Step 4

Divide each term in $4.02840995 L = 9$ by $4.02840995$ and simplify.

Divide each term in $4.02840995 L = 9$ by $4.02840995$ .

$\frac{4.02840995 L}{4.02840995} = \frac{9}{4.02840995}$

Simplify the left side.

Cancel the common factor of $4.02840995$ .

Cancel the common factor.

$\frac{4.02840995 L}{4.02840995} = \frac{9}{4.02840995}$

Divide $L$ by $1$ .

$L = \frac{9}{4.02840995}$

Simplify the right side.

Divide $9$ by $4.02840995$ .

$L = 2.23413209$

Solve for L 3=2pi square root of L/9.8

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