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√2 is a irrational |
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Answer» Assume contary that √2 is rational √2=a/b (where a and b are co primes) √2b=a Squaring both the sides 2b sq.=a sq. eq.1(sq. means square) Now 2 is a factor of a sq. 2 is a factor of a a=2c(c is an integer) From eq. 1 2b sq.=(2c sq.) 2b sq.=4c sq. b sq.=2c sq. 2 is a factor of b sq. 2 is a factor of b 2 is a factod of a and b both.This contradicts arises due to our wrong assumption that √2 is rational. It means √2 is irrational. Hence proved Ya.. |
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