Ex 1.3, 3 - Prove irrational :(i) 1/root(2) (ii) 7root(5) - Ex 1.3

Ex 1.3, 3 (i) - Chapter 1 Class 10 Real Numbers - Part 2


  1. Chapter 1 Class 10 Real Numbers (Term 1)
  2. Serial order wise


Ex 1.3 , 3 Prove that the following are irrationals : 1/โˆš2 We have to prove 1/โˆš2 is irrational Let us assume the opposite, i.e., 1/โˆš2 is rational Hence, 1/โˆš2 can be written in the form ๐‘Ž/๐‘ where a and b (bโ‰  0) are co-prime (no common factor other than 1) Hence, 1/โˆš2 = ๐‘Ž/๐‘ (๐‘ )/๐‘Ž= โˆš2 " " Here, (๐‘ )/๐‘Ž is a rational number But โˆš2 is irrational Since, Rational โ‰  Irrational This is a contradiction โˆด Our assumption is incorrect Hence 1/โˆš2 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.