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Example 11 - Show that  3 root 2 is irrational - Chapter 1 - Examples

  1. Chapter 1 Class 10 Real Numbers
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Example 11 Show that 3โˆš2 is irrational. We have to prove 3โˆš2 is irrational Let us assume the opposite, i.e., 3โˆš2 is rational Hence, 3โˆš2 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, 3โˆš2 = ๐‘Ž/๐‘ โˆš2 " = " 1/3 " ร— " (๐‘Ž )/๐‘ " " โˆš2 " = " (๐‘Ž )/3๐‘ โˆš2 " = " (๐‘Ž )/3๐‘ Here, (๐‘Ž )/3๐‘ is a rational number But โˆš2 is irrational Since, Rational โ‰  Irrational This is a contradiction โˆด Our assumption is incorrect Hence 3โˆš2 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.