Ex 1.2 , 3
Prove that the following are irrationals :
(iii) 6 + β2
We have to prove 6 + β2 is irrational
Let us assume the opposite,
i.e., 6 + β2 is rational
Hence, 6 + β2 can be written in the form π/π
where a and b (bβ 0) are co-prime (no common factor other than 1)
Hence, 6 + β2 = π/π
β2 = π/π - 6
β2 = (π β6π)/π
Here, (π β6π)/π is a rational number
But β5 is irrational
Since, Rational β Irrational
This is a contradiction
β΄ Our assumption is incorrect
Hence, 6 + β2 is irrational
Hence proved.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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