Find the fallacy: $2+2=4-\frac92+\frac92=\sqrt{(4-\frac92)^2}+\frac92=\cdots=5$

Question

I am unable to spot the mathematical technicality error in the riddle below.

Plese elucidate this to me.

Answer 1

The fallacy is in thinking $\sqrt{x^2}=x$. Actually, $\sqrt{x^2}=|x|$.

Answer 2

Since $4-9/2 <0$, it's not true that $4-9/2=\sqrt{(4-9/2)^2}$

Answer 3

I agree with both of these answers - essentially the value in the first square root is $ (-0.5)^2$ , i.e. $0.25$, this stays the same through all values in the subsequent square roots until the last when this is written (correctly) as $0.5^2$.

So all steps look okay, but the overall argument rests on the (incorrect) statement that $x^2 = y^2$ implies $x=y$, a very relevant counter example to this being that $(-0.5)^2$ = $0.5^2$ but $-0.5 <> 0.5$.