Solve for l t=2pi square root of l/9.8

$t = 2 π \sqrt{\frac{l}{9.8}}$

Step 1

Rewrite the equation as $2 π \sqrt{\frac{l}{9.8}} = t$ .

$2 π \sqrt{\frac{l}{9.8}} = t$

Step 2

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

${(2 π \sqrt{\frac{l}{9.8}})}^{2} = t^{2}$

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 ${(\frac{l}{9.8})}^{\frac{1}{2}}$ .

${(2 π {(\frac{l}{9.8})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

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

Multiply by $1$ .

${(2 π {(\frac{1 l}{9.8})}^{\frac{1}{2}})}^{2} = t^{2}$

Factor $9.8$ out of $9.8$ .

${(2 π {(\frac{1 l}{9.8 (1)})}^{\frac{1}{2}})}^{2} = t^{2}$

Separate fractions.

${(2 π {(\frac{1}{9.8} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the expression.

Divide $1$ by $9.8$ .

${(2 π {(0.10204081 \frac{l}{1})}^{\frac{1}{2}})}^{2} = t^{2}$

Divide $l$ by $1$ .

${(2 π {(0.10204081 l)}^{\frac{1}{2}})}^{2} = t^{2}$

Apply the product rule to $0.10204081 l$ .

${(2 π ({0.10204081}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = t^{2}$

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

${(2 π ({({0.31943828}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = t^{2}$

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

${(2 π ({0.31943828}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 π ({0.31943828}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = t^{2}$

Rewrite the expression.

${(2 π ({0.31943828}^{1} l^{\frac{1}{2}}))}^{2} = t^{2}$

Evaluate the exponent.

${(2 π (0.31943828 l^{\frac{1}{2}}))}^{2} = t^{2}$

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

Multiply $0.31943828$ by $2$ .

${(0.63887656 π l^{\frac{1}{2}})}^{2} = t^{2}$

Multiply $0.63887656$ by $π$ .

${(2.00708992 l^{\frac{1}{2}})}^{2} = t^{2}$

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

${2.00708992}^{2} {(l^{\frac{1}{2}})}^{2} = t^{2}$

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

$4.02840995 {(l^{\frac{1}{2}})}^{2} = t^{2}$

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

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

$4.02840995 l^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4.02840995 l^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

$4.02840995 l^{1} = t^{2}$

Simplify.

$4.02840995 l = t^{2}$

Step 4

Divide each term in $4.02840995 l = t^{2}$ by $4.02840995$ and simplify.

Divide each term in $4.02840995 l = t^{2}$ by $4.02840995$ .

$\frac{4.02840995 l}{4.02840995} = \frac{t^{2}}{4.02840995}$

Simplify the left side.

Cancel the common factor of $4.02840995$ .

Cancel the common factor.

$\frac{4.02840995 l}{4.02840995} = \frac{t^{2}}{4.02840995}$

Divide $l$ by $1$ .

$l = \frac{t^{2}}{4.02840995}$

Simplify the right side.

Multiply by $1$ .

$l = \frac{1 t^{2}}{4.02840995}$

Factor $4.02840995$ out of $4.02840995$ .

$l = \frac{1 t^{2}}{4.02840995 (1)}$

Separate fractions.

$l = \frac{1}{4.02840995} \cdot \frac{t^{2}}{1}$

Divide $1$ by $4.02840995$ .

$l = 0.24823689 \frac{t^{2}}{1}$

Divide $t^{2}$ by $1$ .

$l = 0.24823689 t^{2}$

Solve for l t=2pi square root of l/9.8

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