Last updated at April 9, 2021 by Teachoo

Transcript

Ex 1.3 , 3 Prove that the following are irrationals : (iii) 6 + โ2 We have to prove 6 + โ2 is irrational Let us assume the opposite, i.e., 6 + โ2 is rational Hence, 6 + โ2 can be written in the form ๐/๐ where a and b (bโ 0) are co-prime (no common factor other than 1) Hence, 6 + โ2 = ๐/๐ โ2 = ๐/๐ - 6 โ2 = (๐ โ6๐)/๐ Here, (๐ โ6๐)/๐ is a rational number But โ5 is irrational Since, Rational โ Irrational This is a contradiction โด Our assumption is incorrect Hence, 6 + โ2 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 10 years. He provides courses for Maths and Science at Teachoo.