Binomial Theorem: Find Expansion & Approximation of 97^(1/2)

AI Thread Summary
The discussion focuses on finding the first four terms in the expansion of (1 - 3x)^(3/2) using the binomial theorem and approximating 97^(1/2). The initial attempt at the expansion yielded terms that were partially correct, but inaccuracies were noted in the latter terms. An approximation for 97^(1/2) was calculated as 0.848, which participants debated as being slightly off. The conversation also included a contextual hint about the expected value of the square root of 97 based on known square roots of nearby numbers. Overall, the accuracy of the binomial expansion and the approximation method were the main points of contention.
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Homework Statement



Find the first four terms in the expansion of \left(1-3x\right)^{3/2}. By substituting in a suitable value of x, find an approximation to 97^{1/2}.

Homework Equations



The Attempt at a Solution



I used the binomial expansion formula to work the answer and it is 1- 4.5x - (22x2/8) - (247x3/48) + ... .

Is that correct?

I did the second part and i got 0.848. What do you think?

Thanks in advance for any help.
 
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naden1 said:
I used the binomial expansion formula to work the answer and it is 1- 4.5x - (22x2/8) - (247x3/48) + ... .

First two terms are correct, it goes wrong after that. Check your calculations again.
 
naden1 said:
I did the second part and i got 0.848. What do you think?

I think that it's slightly off :wink:
 
Last edited:
naden1 said:
I did the second part and i got 0.848. What do you think?

The positive square root of 100 is 10, and square root 81 is 9. Where would you expect square root of 97 to lie in? :wink:

How did you solve this part?
 
Mentallic said:
I think that it's a slightly off :wink:

Slightly? Wouldn't that be too much? :-p
 

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