# Lorentz factor = 10^6, solving for Beta

1. Sep 17, 2012

### demoncore

1. The problem statement, all variables and given/known data
A particle moves such that its relativistic factor γ equals one million. Find β (=v/c).
Give answer in the form β = 0.999..., with correct number of nines before first non-nine digit. Do not use a calculator

2. Relevant equations

(1-β^2)^(-1/2) = 10^6

3. The attempt at a solution

I've messed around algebraically in a few ways, and tried the binomial approximation, but can't seem to find a way to deal with the β^2 without a calculator.

2. Sep 17, 2012

### TSny

Try to manipulate γ = 106 into an expression for β2 of the form β2 = 1-ε where ε is a very small number that you will determine.

Then β = $\sqrt{1-ε}$. Expand this to first order in ε.