# How do you solve for g in T=2pisqrt(L/g)?

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Kayla Share
Aug 10, 2016

$g = \frac{4 {\pi}^{2} L}{T} ^ 2$

#### Explanation:

$\textcolor{red}{\text{First,}}$ what you want to do is square both sides of the equation to get rid of the square root, since squaring a number is the inverse of taking the square root of a number:

${T}^{2} = {\left(2 \pi\right)}^{2} \sqrt{{\left(\frac{L}{g}\right)}^{2}}$

${T}^{2} = {\left(2 \pi\right)}^{2} \left(\frac{L}{g}\right)$

$\textcolor{b l u e}{\text{Second,}}$ we simplify the ${\left(2 \pi\right)}^{2}$ part so it's easier to read. Remember, when you square something in parenthesis, you are squaring every single term inside:

${T}^{2} = 4 {\pi}^{2} \left(\frac{L}{g}\right)$

$\textcolor{p u r p \le}{\text{third,}}$ multiply both sides by $g$:
$g \times {T}^{2} = 4 {\pi}^{2} \left(\frac{L}{\cancel{\text{g}}}\right) \times \cancel{g}$

$g \times {T}^{2} = 4 {\pi}^{2} L$

$\textcolor{m a r \infty n}{\text{finally,}}$ divide both sides by ${T}^{2}$ to get $g$ by itself:

$\frac{g \times {\cancel{T}}^{2}}{\cancel{T}} ^ 2 = \frac{4 {\pi}^{2} L}{T} ^ 2$

Thus, $g$ is equal to:

$g = \frac{4 {\pi}^{2} L}{T} ^ 2$

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