# Lorentz factor = 10^6, solving for Beta

## Homework Statement

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

## Homework Equations

(1-β^2)^(-1/2) = 10^6

## 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.

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