Dimensional consistency problem, need help

Beginning student striving to learn. The problem was generated by people from the University of Winnipeg. Source: http://ift.tt/1rE3ki4 (this website was actually suggested by a user on the forums who suggested utilizing it as a learning source).

1. The problem statement, all variables and given/known data
Problem is, quote:

The period of a simple pendulum, defined as the time for one complete oscillation, is measured in time units and is given by:

T = 2∏√l/g

where,l is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent; that is, show that the right hand side of this equation gives units of time.

2. Relevant equations
The solution is actually given. The full equation was as follows:

[2∏√l/g]= √L/L/t2. This all equals: √t2 which = T

3. The attempt at a solution

Given the description which is italicized, I understood how they got: √L/L/t2 which ultimately equals T, but I do not understand how "2∏" disappeared so easily in the process of equating T.

My attempt: The italicized description already tells us that "g"= L/t2. Given this information, dividing "L" by L/t2 will result in t2 (all under the square root symbol). Then, the √t2 is T. I get stuck on the conversion process when it comes to 2∏ however.

I’ve thought about it for several minutes, and I still can’t understand how to mathematically describe T and the aforementioned equation including 2∏. Can anyone help? Thank you for your time.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution


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