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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 1.2, 3 (ii) - Chapter 1 Class 10 Real Numbers
Last updated at May 29, 2023 by Teachoo
Transcript
Ex 1.2 , 3 Prove that the following are irrationals : (ii) 7β5 We have to prove 7β5 is irrational Let us assume the opposite, i.e., 7β5 is rational Hence, 7β5 can be written in the form π/π where a and b (bβ 0) are co-prime (no common factor other than 1) Hence, 7β5 = π/π β5 " = " 1/7 " Γ " (π )/π " " β5 " = " (π )/7π Here, (π )/7π is a rational number But β5 is irrational Since, Rational β Irrational This is a contradiction β΄ Our assumption is incorrect Hence 7β5 is irrational Hence proved
