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October 27th, 2008, 04:39 PM   #1
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Square root question

You know when you have an equation such as (x+2)^2 you can simplify it to become x^2+4x+4....is there a way to do that with an equation such as (x+2)^0.5?.....because this would help a lot with integration
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October 27th, 2008, 04:47 PM   #2
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Re: Square root question

In general, I'm afraid the answer is no - but it is possible to get an infinite series expansion. For more info, look at the Binomial Theorem.
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October 27th, 2008, 05:56 PM   #3
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Re: Square root question

Or using Taylor expansion.. Or any other.. But in general, there is no finite formula.
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October 27th, 2008, 07:27 PM   #4
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Re: Square root question

Quote:
Originally Posted by mmmboh
You know when you have an equation such as (x+2)^2 you can simplify it to become x^2+4x+4
Well, for one, I wouldn't do that expansion since (1/3)(d/dx)(x+2)^3 = (x+2)^2dx

And what's wrong with substituting u for sqrt(x+2) in the second?
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October 28th, 2008, 07:51 PM   #5
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Re: Square root question

Quote:
Originally Posted by Dave
Quote:
Originally Posted by mmmboh
You know when you have an equation such as (x+2)^2 you can simplify it to become x^2+4x+4
Well, for one, I wouldn't do that expansion since (1/3)(d/dx)(x+2)^3 = (x+2)^2dx

And what's wrong with substituting u for sqrt(x+2) in the second?
Nothing, I was just using that as an example, but for more complicated equations it would be simpler if we could simplify it in the way I said.
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