Is my method for solving the GRE Relativity Problem correct?

[PsychonautQQ]

Homework Statement

http://grephysics.net/ans/8677/20

So to do this, I solved for the total rest energy of both particles.
The rest energy of Kaon + K = Rest energy of Proton
Rest energy of Proton - Rest Energy of Kaon = K
K = P^2/2m
((Rest Energy of Proton - Rest Energy of Kaon)*(2*Mass of Kaon))^1/2 = P

P = mv/(sqrt(1-v^2/c^2)

If I do this and do all the algebra correct and solve for v, will this method give me the correct answer? I got the wrong answer but I suck at numbers X_x.

I realize after looking at the answers on the website this is a poor way to do this problem with GRE time constraints, I just want to know if this thought process is flawed or not.

 

[Chestermiller]

If the rest energy of a particle is 494 MeV, and its total energy is 938 MeV, what is γ? Since $γ=\frac{1}{\sqrt{1-\beta^2}}$, square both sides and solve for β² in terms of γ². What is the value of β?

 

[PsychonautQQ]

Yeah, I see that this is the best way to do it. I was just wondering if my way works (even though it would take way longer).