Ex 1.3 , 3
Prove that the following are irrationals :
1/√2
We have to prove 1/√2 is irrational
Let us assume the opposite,
i.e., 1/√2 is rational
Hence, 1/√2 can be written in the form 𝑎/𝑏
where a and b (b≠ 0) are co-prime (no common factor other than 1)
Hence, 1/√2 = 𝑎/𝑏 (𝑏 )/𝑎= √2 " "
Here, (𝑏 )/𝑎 is a rational number
But √2 is irrational
Since, Rational ≠ Irrational
This is a contradiction
∴ Our assumption is incorrect
Hence 1/√2 is irrational
Hence proved

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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.