Answer
$\beta= 0.14037076 $
Work Step by Step
lorentz factor $\gamma = 1.01$
We know that the formula for lorentz factor is;
$\gamma = \frac{1}{\sqrt (1-\beta^2)}$
Also, the speed parameter $\beta = \sqrt (1- \frac{1}{\gamma^2})$
We substitute $\gamma$ value i,e 1.01 in above formula and solve:
$\beta = \sqrt (1- \frac{1}{1.01^2})$
$\beta= 0.14037076 $