Question 1207378
<pre>

Suppose a = -2

{{{sqrt(a^2)}}}{{{""=""}}}{{{  sqrt( (-2)^2  )}}}{{{""=""}}}{{{sqrt(4)}}}{{{""=""}}}{{{2}}}{{{""<>""}}}{{{a}}}  Not equal!

But {{{sqrt(a^2)}}}{{{""=""}}}{{{abs(a)}}}  

{{{sqrt(a^2)}}}{{{""=""}}}{{{  sqrt( (-2)^2  )}}}{{{""=""}}}{{{sqrt(4)}}}{{{""=""}}}{{{2}}}{{{""=""}}}{{{abs(-2)}}}{{{""=""}}}{{{a}}}  Equal!

The definition of absolute value is {{{abs(a)}}}{{{""=""}}}{{{sqrt(a^2)}}}

When the radical {{{sqrt("X")}}} is used, it is always either positive
(or zero, in the case {{{sqrt(0)}}}{{{""=""}}}{{{0}}}), but {{{sqrt("X")}}} is never negative!

Although we often say "SQUARE ROOT OF X" when we see {{{sqrt(X)}}}, 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</pre>