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Ex 1.3, 3 - Prove irrational :(i) 1/root(2) (ii) 7root(5) - Ex 1.3

Ex 1.3, 3 (i) - Chapter 1 Class 10 Real Numbers - Part 2

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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 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.