Intuition behind errors

I want to ask a question about the multiplication of two variables and the error associated with the process. 


I was learning about calculating errors in the physical labs at school and was taught that the following formula was used to calculate errors:



> 
> $\frac{\triangle Z}{Z} = \frac{\triangle A}{A} + \frac{\triangle B}{B}$
> 
> 
> 


This made sense, given that we are in essence calculating percentage uncertainties and these are added when calculating the uncertainty of Z. 


However, in my current undergraduate lab, we square each term:



> 
> $(\frac{\triangle Z}{Z})^2 = (\frac{\triangle A}{A})^2 + (\frac{\triangle B}{B})^2$
> 
> 
> 


and I cannot find any reference to explain the purpose of squaring the values. 


Why do we square each term as above?


