Why relativistic momentum equals the following?

[Foruer]

In a solution to a problem we were given, it is written that a positron momentum with energy of 2mc²
(where γ=2) is √(γ²-1)*mc = √(4-1)*mc = √3*mc

How did they get that P=√(γ²-1)*mc?

 

[Nathanael]

You are familiar with p = ϒmv right?
And also with ϒ = 1/√(1-(v/c)²) right?

Eliminate v from the two equations and what do you get?

 

[Foruer]

What I get is the answer thank you

 

[Orodruin]

While it gives you the right answer, it is much simpler to use the energy-momentum relation $E^2 - p^2 c^2 = m^2 c^4$ and just solve for $p$.