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Prove the no is irrational no √2 |
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Answer» Let us take √2 is rational We can take x and y √2 = x/y Suppose x and s have a common factor other than 1. Then you have to divide by the common factor √2 = a/ b, where a and b are coprime.So b √2 = aOn sq. Both side 2b ka 2 = a ka 22 divide a ka 2.So we take another integer c.a = 2cWe get 2b ka 2 = 4c ka 2 b ka 2 = 2c ka 2That means 2 divide b ka 2 and so 2 divides b. Therefore a and b have at least 2 as a common factor.This contradiction has arisen because of our incorrect assumption that √ 2 is rational.So, we conclude that √2 is irrational. See in NCERT |
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