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
