Example 10 - Show that  5 - root 3 is irrational - Chapter 1 - Examples

  1. Chapter 1 Class 10 Real Numbers
  2. Serial order wise
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Example 10 Show that 5 - √3 is irrational. We have to prove 5 - √3 is irrational Let us assume the opposite, i.e., 5 - √3 is rational Hence, 5 - √3 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, 5 - √3 = π‘Ž/𝑏 βˆ’βˆš3 = π‘Ž/𝑏 - 5 βˆ’βˆš3 = (π‘Ž βˆ’5𝑏)/𝑏 βˆ’ √3 = (π‘Ž βˆ’ 5𝑏)/𝑏 √3 = βˆ’((π‘Ž βˆ’ 5𝑏)/𝑏) √3 = (5𝑏 βˆ’ π‘Ž )/𝑏 Here, (βˆ’π‘Ž +5𝑏)/𝑏 is a rational number But √3 is irrational Since, Rational β‰  Irrational This is a contradiction ∴ Our assumption is incorrect Hence, 5 - √3 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.