Answer
$\beta = 0.99999950 $
Work Step by Step
lorentz factor $\gamma=1000$
We know that formula for lorentz factor is;
$\gamma =\frac{1}{\sqrt (1-\frac{1}{\beta^2})}$
Also, the speed parameter $\beta =\sqrt (1-\frac{1}{\gamma^2})$
We substitute $\gamma$ value i,e 1000 in above formula and solve;
$\beta =\sqrt (1-\frac{1}{1000^2})$
$\beta = 0.99999950 $
