At what speed does the classical momentum, p=mv, give an error, when compared with the relativistic momentum, of 1.35 % ?

The classical momentum is given by:

where m is the particle mass and v its velocity, while the relativistic momentum is given by:

where 
  (1)
is the relativistic factor, with c being the speed of light.

The condition given by the problem (error of 1.35%) can be rewritten as

which means

and since , this also means that


Now let's re-arrange eq.(1), and we get

and if we use  as we found before, and , we find the corresponding velocity:

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