Speed parameter β and Lorentz factor γ

[rlc]

Homework Statement

Find the speed parameter β and Lorentz factor γ for an electron that has a kinetic energy of:

a) 6.00 keV
b) 2.00 MeV
c) 4.00 GeV

Homework Equations

KE=(γ-1)*511 KeV
SQRT(1/(1-β^2))=γ

The Attempt at a Solution

a) 6 KeV=(y-1)*511
y=1.0117
1.0117=SQRT(1/(1-β^2))
β=0.152

b) 2 MeV=(y-1)*0.511
y=4.91
4.91=SQRT(1/(1-β^2))
β=0.979

c) 4000 MeV=(y-1)*0.511
y=7828
My issue with this problem is I can't figure out how to calculate β. I was able to calculate the other betas by guessing and checking what beta was...I don't know how to simplify the equation to make solving for beta easier.
I can't use this method for this particular problem because y is so large. If someone could point out to me where my issue is, and how to go about getting around this problem, I would be very thankful.

 

[phyzguy]

You have:
$$\gamma = \sqrt{\frac{1}{1-\beta^2}}$$
If you square both sides you have:
$$\gamma^2 = \frac{1}{1-\beta^2}$$

Can't you take this and solve for β in terms of γ?

 

[Noctisdark]

Nope your just fine,
√(1/1-β^2) = γ
Express β in function of γ and you'll get it,
Hope this helps :)

 

[rlc]

Thank you! The answer ended up being 1.00
It's pretty clear I haven't taken a math class in a while... :)