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Last updated at May 29, 2018 by Teachoo

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Example 11 Show that 3โ2 is irrational. We have to prove 3โ2 is irrational Let us assume the opposite, i.e., 3โ2 is rational Hence, 3โ2 can be written in the form ๐/๐ where a and b (bโ 0) are co-prime (no common factor other than 1) Hence, 3โ2 = ๐/๐ โ2 " = " 1/3 " ร " (๐ )/๐ " " โ2 " = " (๐ )/3๐ โ2 " = " (๐ )/3๐ Here, (๐ )/3๐ is a rational number But โ2 is irrational Since, Rational โ Irrational This is a contradiction โด Our assumption is incorrect Hence 3โ2 is irrational Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.