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**Malik641****Member**- Registered: 2005-10-18
- Posts: 3

Hey guys,

my question is how do you apply the binomial theorem when the quantity is raised to a non-integer value?

Specifically, (a+b)^(1/2)

I had a homework problem for my mechanics of materials class, and I got "x" far. I checked the answer, and they went further with it, calling out the Binomial Theorem as the reason for taking it a step further.

my answer was:

[1+(dL/L)]^(1/2) - 1

then their answer was (same as mine, then one step further):

1 + (1/2)(dL/L) ... - 1 "Binomial Theorem"

= (0.5*dL)/L

I don't know why this is racking my brain so hard...I think it's because of the 3 dots "..."

Thanks in Advanced

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**Dross****Member**- Registered: 2006-08-24
- Posts: 325

Malik641 wrote:

my answer was:

[1+(dL/L)]^(1/2) - 1

then their answer was (same as mine, then one step further):

1 + (1/2)(dL/L) ... - 1 "Binomial Theorem"

= (0.5*dL)/L

Erm... that doesn't look much like the same answer to me! Your answer is:

While their answer is:

Which, if you cancel the first and last terms, gets you to their answer, plus a load of dots....?

Perhaps if you told us the original question, along with how you got to your answer, we could help you out a bit more...

Bad speling makes me [sic]

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**Malik641****Member**- Registered: 2005-10-18
- Posts: 3

I'm sorry, but I don't see how the square root of dL/L gives you (1/2)(dL/L)......?????

Dross wrote:

Perhaps if you told us the original question, along with how you got to your answer, we could help you out a bit more...

Perhaps...I thought my original question was sufficient enough, though.

I got as far as they did (the same way) up to the part where:

Eab = (1 + (dL/L))^(1/2) - 1

Take a look at the image (link). That's everything.

*Last edited by Malik641 (2006-09-21 14:49:33)*

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