

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Examples
Example 2
Example 3
Example 4 Important
Example 5 Important
Example 6 Important You are here
Example 7
Prove that root 2 is Irrational
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Deleted for CBSE Board 2024 Exams
Question 4 Important Deleted for CBSE Board 2024 Exams
Last updated at June 23, 2023 by Teachoo
Example 6 Show that 5 − √3 is irrational. We have to prove 5 − √3 is irrational Let us assume the opposite, i.e., 5 − √𝟑 is rational Hence, 5 − √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 − √𝟑 = 𝒂/𝒃 −√3 = 𝑎/𝑏 - 5 −√3 = (𝑎 − 5𝑏)/𝑏 − √3 = (𝑎 − 5𝑏)/𝑏 √3 = −((𝑎 − 5𝑏)/𝑏) √𝟑 = (𝟓𝒃 − 𝒂 )/𝒃 Here, (5𝑏 − 𝑎)/𝑏 is a rational number But √3 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Therefore, 5 - √𝟑 is irrational Hence proved.