M = 2 - square_root(u - 3)
u = (v - 2)^2 + 3
Prove that M = v.
Your use of the square root is incorrect. $\displaystyle \sqrt{x^2}= |x|$, NOT x.
So $\displaystyle \sqrt{(v- 2)^2}= |v- 2|$. Whether that is equal to v- 2 or 2- v depends upon whether $\displaystyle v\ge 2$ or $\displaystyle v< 2$.
If you are not told whether v is larger than 2 or not, the best you can say is that
$\displaystyle 2- \sqrt{((v- 2)^2+ 3)- 3}= 2- \sqrt{(v- 2)^2}= 2- |v- 2|$. That is either v (if $\displaystyle v\ge 2$) or 4- v (if $\displaystyle v\le 2$).