Prove that 6 + root 2 is irrational [Video] - Class 10 Maths - Teachoo

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

  1. Chapter 1 Class 10 Real Numbers
  2. Serial order wise

Transcript

Ex 1.3 , 3 Prove that the following are irrationals : (iii) 6 + โˆš2 We have to prove 6 + โˆš2 is irrational Let us assume the opposite, i.e., 6 + โˆš2 is rational Hence, 6 + 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, 6 + โˆš2 = ๐‘Ž/๐‘ โˆš2 = ๐‘Ž/๐‘ - 6 โˆš2 = (๐‘Ž โˆ’6๐‘)/๐‘ Here, (๐‘Ž โˆ’6๐‘)/๐‘ is a rational number But โˆš5 is irrational Since, Rational โ‰  Irrational This is a contradiction โˆด Our assumption is incorrect Hence, 6 + 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.