Show the equation of simple pendulum to be dimensionally consistent

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.