please help me understand this statement that i have in my lecture notes

If for all r $\displaystyle \in$ R there exists some $\displaystyle x \in R$ such that $\displaystyle x^2 = r$ then the same statement is true in $\displaystyle \varphi$ [R].

This shows that there is no homomorphism that maps the Complex numbersontothe real numbers (surjective)

i'm not quite sure how it can be used to disprove some onto homomorphisms' existences like the one above