Question 36954
{{{(sqrt(x))^2=x}}} is an identity.


ILLUSTRATION: 
Suppose x = 8, then {{{sqrt(x)}}} = {{{sqrt(8)}}} = either {{{2sqrt(2)}}} or {{{-2sqrt(2)}}}.
Now, as both {{{(2sqrt(2))^2}}} and {{{(-2sqrt(2))^2}}} are equal to 8 (= x) hence the truth of the statement made above can easily be verified.


However, if x be a negative number, say, x = -4. 
Then {{{sqrt(-4)}}} is imaginery and equals {{{2i}}} [where i = {{{sqrt(-1)}}}]. So {{{(sqrt(x))^2}}} = {{{(2i)^2}}} = {{{4i^2}}} = -4 = x.
Thus, the proposition is also valid for negative real values of 'x'.