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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Does anyone know if there is ANY identity for sqrt ( a + b) ? It would be super usefull for integration and many other things.

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Or try to prove that no identity exists.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I think not.

IPBLE: Increasing Performance By Lowering Expectations.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

The only thing I've come up with is if a and b are both positive, sqrt (a + b) is the hypotenuse of a right triangle whose legs are sqrt(a), sqrt (b). The only way I know to solve this without using the pythegorean theorem is to find θ.

θ = arctan (sqrt b / sqrt a),

c = sqrt b/ sin θ OR sqrt a / cos θ = sqrt ( a + b)

but really all we get is sqrt (a + b) = sqrt b / sin [ arctan (sqrt b / sqrt a) ]

But as a substitution identity thats pretty worthless as it only makes it more complicated.

*Last edited by mikau (2006-05-16 04:07:50)*

A logarithm is just a misspelled algorithm.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I put a square in the center of a square and tried solving for stuff, but after quadratic formula, it came back to sqrt(a + b) again!

*Last edited by John E. Franklin (2006-05-16 09:28:32)*

**igloo** **myrtilles** **fourmis**

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Yeah I wasted a lot of time going in circles with this one.

A logarithm is just a misspelled algorithm.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

This may be helpful (it requires only

and :.

*Last edited by krassi_holmz (2006-05-19 01:02:31)*

IPBLE: Increasing Performance By Lowering Expectations.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Yeah but they are still a sum inside a radical. Ideally an identity similar to something like sin ( a + b) would be nice. For instance: sqrt ( a + b) = sqrt a sqrt b - 1/sqrt b sqrt a or something like that, that seperates them into individual squareroots.

A logarithm is just a misspelled algorithm.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Yeah, I know.

But I don't think we'll go further than

IPBLE: Increasing Performance By Lowering Expectations.

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