Question 1208654
For an example, let's say {{{a=-1}}}. Then, {{{sqrt(a^2)=sqrt((-1)^2)=sqrt(1)=1}}}, which is not equal to -1.<br>
Note that the square root function always takes the principal square root (the nonnegative one). If {{{a}}} is positive, then {{{sqrt(a^2)}}} will still be {{{a}}}, since that is the principal square root. If {{{a}}} is negative, then {{{sqrt(a^2)}}} will be {{{-a}}}, since the two square roots are {{{a}}} and {{{-a}}}, and {{{-a}}} is the principal square root. ({{{a}}} is negative, so {{{-a}}} is positive). If {{{a}}} is 0, then {{{sqrt(a^2)}}} is also just {{{a}}}. Note that this is the exact definition of |a|. The absolute value function leaves positive numbers and zero unchanged, while taking the negative of negative numbers to make them positive. (same thing the square root function did).