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Question 26 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 13, 2024 by Teachoo

Given that √3 is irrational, prove that 5 + 2√3 is irrational

This question is Similar to Question-27 CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Transcript

Question 26 Given that √3 is irrational, prove that 5 + 2√3 is irrationalWe have to prove 5 + 2√3 is irrational Let us assume the opposite, i.e., 5 + 2√𝟑 is rational Hence, 5 + 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, 5 + 2√𝟑 = 𝒂/𝒃 2√3 = 𝑎/𝑏 − 5 √3 = 𝑎/2𝑏 − 5/2 √𝟑 = (𝒂 − 𝟓𝒃)/𝟐𝒃 Here, (𝒂 − 𝟓𝒃)/𝟐𝒃 is a rational number But √3 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Hence, 5 + 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