Prove that 7 root 5 is irrational (with Video) - Class 10 Maths

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

 

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

Transcript

Ex 1.3 , 3 Prove that the following are irrationals : (ii) 7โˆš5 We have to prove 7โˆš5 is irrational Let us assume the opposite, i.e., 7โˆš5 is rational Hence, 7โˆš5 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, 7โˆš5 = ๐‘Ž/๐‘ โˆš5 " = " 1/7 " ร— " (๐‘Ž )/๐‘ " " โˆš5 " = " (๐‘Ž )/7๐‘ Here, (๐‘Ž )/7๐‘ is a rational number But โˆš5 is irrational Since, Rational โ‰  Irrational This is a contradiction โˆด Our assumption is incorrect Hence 7โˆš5 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.