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Number Theory homework. I'm supposed to prove that the value

2^.5 + 3^.5

is irrational by finding a monic polynomial that the aforementioned number is a root of. This would be trivial if I were supposed to prove that just 2^.5 was irrational because its monic polynomial equation would be x^2 -2 = 0.

But I can't just raise 2^.5 + 3^.5 to a power and then subtract it to get my desired polynomial because all coefficients of a monic polynomial have to be integers, and 2^.5 + 3^.5 is obviously not an integer.

What method should I use to go about finding such a monic polynomial?

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# Homework Help: Finding a monic polynomial with 2^.5 + 3^.5 as a root

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