SOLUTION: Give an example to show that sqrt{a^2} is not equal to a. Use it to explain why sqrt{a^2} = |a|.

Suppose a = -2

  Not equal!

But   

  Equal!

The definition of absolute value is 

When the radical  is used, it is always either positive
(or zero, in the case ), but  is never negative!

Although we often say "SQUARE ROOT OF X" when we see , we
really should say "NON-NEGATIVE SQUARE ROOT OF X".

[It's like in geometry, we often say "line" when we really should say
 "line segment".]

Edwin