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Acceleration due to gravity above Earth

"How far above the Earth's surface will the acceleration due to gravity be a quarter of what it is on the surface?"

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?

Solution Preview

<br>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.
<br>Method 1
<br>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 earth. Thus g ...