Ex 1.2 , 3
Prove that the following are irrationals :
(ii) 7β5
We have to prove 7β5 is irrational
Let us assume the opposite,
i.e., 7β5 is rational
Hence, 7β5 can be written in the form π/π
where a and b (bβ 0) are co-prime (no common factor other than 1)
Hence, 7β5 = π/π
β5 " = " 1/7 " Γ " (π )/π " "
β5 " = " (π )/7π
Here, (π )/7π is a rational number
But β5 is irrational
Since, Rational β Irrational
This is a contradiction
β΄ Our assumption is incorrect
Hence 7β5 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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