I tried to use the g' = (G * m) / r^2 equation (with the mass of the earth as "m") because it was used with a somewhat similar problem in my book about the value of g on the top of Mount Everest, but I came up with a ridiculous number.
Can you tell me how to do this problem correctly?
To begin with, I'd like to say you were on the right track when you used g=G*m/r^2 but I guess something went wrong in your calculation. I'm going to suggest 2 approaches: one of them quick and intuitive, the other a more brute force method that will succeed if the first way doesn't occur to you.
since G and m are constants regardless of your height above the earth, the only variable here is "r", ie distance to the centre of ...
The acceleration due to gravity above the Earth is determined. How far above the earth's surface will the acceleration due to gravity be a quarter of what it is on the surface is computed.