How to prove that <msqrt>

Armeninilu 2022-06-27 Answered
How to prove that 3 is an irrational number?
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Answers (2)

Leland Ochoa
Answered 2022-06-28 Author has 25 answers
Let 3 = p q , p , q relatively prime. 3 = p 2 q 2 , so 3 divides p and so on.

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aligass2004yi
Answered 2022-06-29 Author has 7 answers
Let 3 = a b , where a and b have no common factors besides 1

As 3 b 2 = a 2 so a 2 is a multiple of 3, and hence a should be a multiple of 3. Let a = 3 k, then b 2 = 3 k 2 , and b must also be a multiple of three. You will arrive at a contradiction to the earlier assumption that a and b have no common factors.

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