Question

prove that √3 is irrational number​

Answer 1

Say 3–√3 is rational. Then 3–√3 can be represented as abab, where a and b have no common factors.

So 3=a2b23=a2b2 and 3b2=a23b2=a2. Now a2a2 must be divisible by 33, but then so must aa(fundamental theorem of arithmetic). So we have 3b2=(3k)23b2=(3k)2 and 3b2=9k23b2=9k2 or even b2=3k2b2=3k2and now we have a contradiction.

What is the contradiction?

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answeredSep 14 '14 at 4:06



Chantry Cargill

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editedSep 14 '14 at 4:12

@The-Duderino By the way, the proof for 6–√

Answer 2

Step-by-step explanation:

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