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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Last updated at May 29, 2023 by Teachoo
Ex 1.2 , 3 Prove that the following are irrationals : (iii) 6 + β2 We have to prove 6 + β2 is irrational Let us assume the opposite, i.e., 6 + β2 is rational Hence, 6 + β2 can be written in the form π/π where a and b (bβ 0) are co-prime (no common factor other than 1) Hence, 6 + β2 = π/π β2 = π/π - 6 β2 = (π β6π)/π Here, (π β6π)/π is a rational number But β5 is irrational Since, Rational β Irrational This is a contradiction β΄ Our assumption is incorrect Hence, 6 + β2 is irrational Hence proved.