1. ## Binomial expansion question

Prove that , if x is so small that terms in x^3 and higher powers may be neglected, then .

By substituting a suitable value of x in your result, show that (11)^1/2 is approximately equal to 663/200.

I can solve the first part, but i have difficulty in the second part (show that (11)^1/2 is approximately equal to 663/200). Can anyone help me? Thanks.

2. If $\displaystyle \displaystyle \sqrt{11} = \sqrt{\frac{1 + x}{1 - x}}$, then what is $\displaystyle \displaystyle x$?

3. Originally Posted by Prove It
If $\displaystyle \displaystyle \sqrt{11} = \sqrt{\frac{1 + x}{1 - x}}$, then what is $\displaystyle \displaystyle x$?
By solving that, i get x= 5/6. Substituting x=5/6 into , i get (11)^1/2=157/72 which is incorrect...

4. Indeed, I was getting this too. I think there is something wrong with the question. The issue is surely due to the fact that 5/6 is not small enough for x^3 and higher powers to be neglected.

Either that, or I'm missing something.

5. "Approximately equal" is a loose term. Yes, using x= 5/6 gives $\displaystyle 1+ 5/6+ 25/72= 1.18$ while $\displaystyle \sqrt{11}= .32$ approximately. That's not very close but then, as Unknown008 said, 5/6 is not all that "small"! $\displaystyle \left(\frac{5}{6}\right)^3$ is larger than 1/2- hardly "negligible".

6. $\displaystyle \sqrt{11} = 3.316...$

$\displaystyle 1 + \dfrac56 + \dfrac12 \left(\dfrac{25}{36}\right) = 2.18...$

It must eirler be very late, or very early where you are HallsofIvy

7. Hint: If you knew the square root of 11/9, you could easily compute the square root of 11.

8. Originally Posted by awkward
Hint: If you knew the square root of 11/9, you could easily compute the square root of 11.
But how do i get 'square root of 11/9'? And how to compute 'square root of 11' after i get 'square root of 11/9'? Please enlighten me..

9. Originally Posted by MichaelLight
But how do i get 'square root of 11/9'?
The same way you found the square root of 11 previously.

And how to compute 'square root of 11' after i get 'square root of 11/9'? Please enlighten me..
Simplify $\displaystyle \sqrt{\frac{11}{9}}$.