Binomial theorem

1. Jun 23, 2012

1. The problem statement, all variables and given/known data

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 $97^{1/2}$.

2. Relevant equations

3. 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.

2. Jun 23, 2012

Saitama

First two terms are correct, it goes wrong after that. Check your calculations again.

3. Jun 23, 2012

Mentallic

I think that it's slightly off

Last edited: Jun 23, 2012
4. Jun 23, 2012

Infinitum

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?

How did you solve this part?

5. Jun 23, 2012

Saitama

Slightly? Wouldn't that be too much? :tongue: