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.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.