Solve for l t=2pi square root of l/980

$t = 2 π \sqrt{\frac{l}{980}}$

Rewrite the equation as $2 π \sqrt{\frac{l}{980}} = t$ .

$2 π \sqrt{\frac{l}{980}} = t$

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

${(2 π \sqrt{\frac{l}{980}})}^{2} = t^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{980}}$ as ${(\frac{l}{980})}^{\frac{1}{2}}$ .

${(2 π {(\frac{l}{980})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

Simplify ${(2 π {(\frac{l}{980})}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $\frac{l}{980}$ .

${(2 π \frac{l^{\frac{1}{2}}}{980^{\frac{1}{2}}})}^{2} = t^{2}$

Multiply $2 π \frac{l^{\frac{1}{2}}}{980^{\frac{1}{2}}}$ .

Combine $\frac{l^{\frac{1}{2}}}{980^{\frac{1}{2}}}$ and $2$ .

${(\frac{l^{\frac{1}{2}} \cdot 2}{980^{\frac{1}{2}}} π)}^{2} = t^{2}$

Combine $\frac{l^{\frac{1}{2}} \cdot 2}{980^{\frac{1}{2}}}$ and $π$ .

${(\frac{l^{\frac{1}{2}} \cdot 2 π}{980^{\frac{1}{2}}})}^{2} = t^{2}$

Move $2$ to the left of $l^{\frac{1}{2}}$ .

${(\frac{2 \cdot l^{\frac{1}{2}} π}{980^{\frac{1}{2}}})}^{2} = t^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 l^{\frac{1}{2}} π}{980^{\frac{1}{2}}}$ .

$\frac{{(2 l^{\frac{1}{2}} π)}^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

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

$\frac{{(2 l^{\frac{1}{2}})}^{2} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

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

$\frac{2^{2} {(l^{\frac{1}{2}})}^{2} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

Simplify the numerator.

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

$\frac{4 {(l^{\frac{1}{2}})}^{2} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

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

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

$\frac{4 l^{\frac{1}{2} \cdot 2} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 l^{\frac{1}{2} \cdot 2} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

Rewrite the expression.

$\frac{4 l^{1} π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

Simplify.

$\frac{4 l π^{2}}{{(980^{\frac{1}{2}})}^{2}} = t^{2}$

Simplify the denominator.

Multiply the exponents in ${(980^{\frac{1}{2}})}^{2}$ .

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

$\frac{4 l π^{2}}{980^{\frac{1}{2} \cdot 2}} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 l π^{2}}{980^{\frac{1}{2} \cdot 2}} = t^{2}$

Rewrite the expression.

$\frac{4 l π^{2}}{980^{1}} = t^{2}$

Evaluate the exponent.

$\frac{4 l π^{2}}{980} = t^{2}$

Cancel the common factor of $4$ and $980$ .

Factor $4$ out of $4 l π^{2}$ .

$\frac{4 (l π^{2})}{980} = t^{2}$

Cancel the common factors.

Factor $4$ out of $980$ .

$\frac{4 (l π^{2})}{4 \cdot 245} = t^{2}$

Cancel the common factor.

$\frac{4 (l π^{2})}{4 \cdot 245} = t^{2}$

Rewrite the expression.

$\frac{l π^{2}}{245} = t^{2}$

Solve for $l$ .

Multiply both sides of the equation by $\frac{245}{π^{2}}$ .

$\frac{245}{π^{2}} \cdot \frac{l π^{2}}{245} = \frac{245}{π^{2}} t^{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{245}{π^{2}} \cdot \frac{l π^{2}}{245}$ .

Combine.

$\frac{245 (l π^{2})}{π^{2} \cdot 245} = \frac{245}{π^{2}} t^{2}$

Cancel the common factor of $245$ .

Cancel the common factor.

$\frac{245 (l π^{2})}{π^{2} \cdot 245} = \frac{245}{π^{2}} t^{2}$

Rewrite the expression.

$\frac{l π^{2}}{π^{2}} = \frac{245}{π^{2}} t^{2}$

Cancel the common factor of $π^{2}$ .

Cancel the common factor.

$\frac{l π^{2}}{π^{2}} = \frac{245}{π^{2}} t^{2}$

Divide $l$ by $1$ .

$l = \frac{245}{π^{2}} t^{2}$

Simplify the right side.

Combine $\frac{245}{π^{2}}$ and $t^{2}$ .

$l = \frac{245 t^{2}}{π^{2}}$

Solve for l t=2pi square root of l/980

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