T is in seconds (s)
2pi is dimensionless
L is in meters (m)
g is in meters per second squared (m/s^2)
so you can write the equation for the period of the simple pendulum in its units...
s=sqrt(m/(m/s^2))
simplify
s=sqrt(m*s^2*1/m) cancelling the m's
s=sqrt(s^2)
s=s
therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.
