Saw this question which was asked at a job interview for an engineer on Quora,
It’s often useful to be able to make approximations quickly.
If you make a somewhat accurate fast approximation, sometimes you can tell whether something is a good idea or bad idea without investing much more time.
With an engineering background, it might be assumed that you have done many calculations and are pretty good at making them.
Many people have done a lot of calculations without a calculator, Google, Mathematica, etc.
They probably wanted to see your response to the question as well as getting an idea of your sense of numbers.
If you said 42, in this case, it would not be the answer to get you a job. Though it might get a laugh.
Saying 1,000 would be somewhat reasonable and the right order of magnitude since 1,000^2 is 1,000,000.
10,000 would be too big and not the right order of magnitude.
2,000^2 would be 4,000,000 so it’s getting more accurate.
If you knew that 1,000^2 is 1,000,000 and that you would still need to get the root of 5 and said that the answer is exactly √5 * 1000, the interviewer would probably be impressed.
If you said something that was an approximation of that and pretty close, that would probably also go over well.
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