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

  1. Chapter 1 Class 10 Real Numbers
  2. Serial order wise
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Example 11 Show that 3√2 is irrational. We have to prove 3√2 is irrational Let us assume the opposite, i.e., 3√2 is rational Hence, 3√2 can be written in the form π‘Ž/𝑏 where a and b (bβ‰  0) are co-prime (no common factor other than 1) Hence, 3√2 = π‘Ž/𝑏 √2 " = " 1/3 " Γ— " (π‘Ž )/𝑏 " " √2 " = " (π‘Ž )/3𝑏 √2 " = " (π‘Ž )/3𝑏 Here, (π‘Ž )/3𝑏 is a rational number But √2 is irrational Since, Rational β‰  Irrational This is a contradiction ∴ Our assumption is incorrect Hence 3√2 is irrational Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.