SOLUTION: the conjugate of sqare_root(2)-square_root(3) is: square_root(2)+square_root(3). But can it be: -sqare_root(2)-square_root(3)? please note that even if they are not comp

Algebra ->  Algebra  -> Permutations -> SOLUTION: the conjugate of sqare_root(2)-square_root(3) is: square_root(2)+square_root(3). But can it be: -sqare_root(2)-square_root(3)? please note that even if they are not comp      Log On

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Question 6558: the conjugate of
sqare_root(2)-square_root(3) is:
square_root(2)+square_root(3).
But can it be:
-sqare_root(2)-square_root(3)?

please note that even if they are not complex numbers ,
they are surds.
For surds conjugate of 2-square_root(3) is 2+square_root(3),
so why not -2-square_root(3)?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i have looked on the web and not found much at all, however one pdf had an example where it multiplied by a "surd conjugate". Looking into this, it looks like x%2Bsqrt%28y%29 has the conjugate x-sqrt%28y%29. As for why...that is the definition of the conjugate. Simple as that.

As for the reason behind using a conjugate...it removes any irrational/surd parts, since %28x%2Bsqrt%28y%29%29%28x%2Bsqrt%28y%29%29 is x%5E2+-+x%2Asqrt%28y%29+%2B+x%2Asqrt%28y%29+-+y --> x%5E2+-+y.

Jon.