SOLUTION: evaluate without using a calculator, using binomial theorem, 1) 4th root (624) 2) 1/(1+x)^1/2

Question 825831: evaluate without using a calculator, using binomial theorem,
1) 4th root (624)
2) 1/(1+x)^1/2
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1) I am not sure exactly what you are expected to do to evaluate without using a calculator, using binomial theorem, but this is what I would do.
and
Since 624 is so close to 625, i would expect to be very close to 5, so let's try 4.9.

Since 624 is much closer to 625 than to 576.48, I would expect to be much closer to 5 than to 4.9, so I would try 4.99.

= about
At this point, knowing that and , I would estimate by assuming that is approximately linear between 4.990 and 5.000.

2) There is nothing that can be evaluated in
, since we do not have a value for .
That expression can be rationalized as

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