Question 27 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Prove that 2 – √3 is irrational, given that √3 is irrational.

Prove that 2-√3 is irrational, given that √3 is irrational [Video]

Question 27 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2

Question 27 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 3

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Question 27 Prove that 2 – √3 is irrational, given that √3 is irrational. We have to prove 2 – √3 is irrational Let us assume the opposite, i.e., 2 – √𝟑 is rational Hence, 2 – √3 can be written in the form 𝑎/𝑏 where a and b (b≠ 0) are co-prime (no common factor other than 1) Hence, 2 – √𝟑 = 𝒂/𝒃 −√3 = 𝑎/𝑏 − 2 √3 = (−𝑎)/𝑏 + 2 Here, (−𝑎 + 2𝑏)/𝑏 is a rational number But √3 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Hence, 2 – √𝟑 is irrational Hence proved.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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