Math Is Fun Forum

mikau

Member

Registered: 2005-08-22

Posts: 1,504

identity for sqrt (a + b)

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

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A logarithm is just a misspelled algorithm.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: identity for sqrt (a + b)

Or try to prove that no identity exists.

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"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..."

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: identity for sqrt (a + b)

I think not.

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IPBLE:  Increasing Performance By Lowering Expectations.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: identity for sqrt (a + b)

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)

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A logarithm is just a misspelled algorithm.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: identity for sqrt (a + b)

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)

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igloo myrtilles fourmis

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: identity for sqrt (a + b)

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

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A logarithm is just a misspelled algorithm.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: identity for sqrt (a + b)

This may be helpful (it requires only

and

:

.

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

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IPBLE:  Increasing Performance By Lowering Expectations.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: identity for sqrt (a + b)

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.

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A logarithm is just a misspelled algorithm.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: identity for sqrt (a + b)

Yeah, I know.
But I don't think we'll go further than

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IPBLE:  Increasing Performance By Lowering Expectations.