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

[naden1]

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.

 

[Saitama]

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.

 

[Mentallic]

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

I think that it's slightly off

 

[Infinitum]

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?

How did you solve this part?

 

[Saitama]

I think that it's a slightly off

Slightly? Wouldn't that be too much?