Prove that 2 – √3 is irrational, given that √3 is irrational.
Last updated at Oct. 26, 2020 by
Transcript
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.
CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
Question 1 (Choice - 2)
Question 2
Question 3 Important
Question 4
Question 5 (Choice - 1)
Question 5 (Choice - 2)
Question 6
Question 7 (Choice - 1)
Question 7 (Choice - 2)
Question 8 Important
Question 9 (Choice - 1)
Question 9 (Choice - 2) Important
Question 10
Question 11 Important
Question 12
Question 13
Question 14
Question 15
Question 16 (Choice - 1)
Question 16 (Choice - 2)
Question 17 (Case Based Question) Important
Question 18 (Case Based Question) Important
Question 19 (Case Based Question) Important
Question 20 (Case Based Question) Important
Question 21 Important
Question 22 (Choice - 1)
Question 22 (Choice - 2)
Question 23 Important
Question 24
Question 25 (Choice - 1)
Question 25 (Choice - 2)
Question 26 Important
Question 27 You are here
Question 28 (Choice - 1)
Question 28 (Choice - 2)
Question 29 Important
Question 30 (Choice - 1) Important
Question 30 (Choice - 2)
Question 31 Important
Question 32
Question 33 Important
Question 34 (Choice - 1)
Question 34 (Choice - 2)
Question 35 Important
Question 36 Important
CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
About the Author