Last updated at Aug. 2, 2021 by Teachoo

Transcript

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 / where a and b (b 0) are co-prime (no common factor other than 1) Hence, 5 - 3 = / 3 = / - 5 3 = ( 5 )/ 3 = ( 5 )/ 3 = (( 5 )/ ) 3 = (5 )/ Here, ( +5 )/ is a rational number But 3 is irrational Since, Rational Irrational This is a contradiction Our assumption is incorrect Hence, 5 - 3 is irrational Hence proved.

Chapter 1 Class 10 Real Numbers (Term 1)

Serial order wise

About the Author

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.