Prove that 3√2 is irrational

Asked by goyalmanvi37 | 22nd May, 2021, 08:56: PM

Expert Answer:

begin mathsize 16px style Let space us space assume space that space 3 square root of 2 space is space straight a space rational space number.
rightwards double arrow 3 square root of 2 space equals straight a over straight b comma space where space straight a space and space straight b space are space co space minus space prime space integers space comma space straight b space not equal to 0.
rightwards double arrow square root of 2 space equals space fraction numerator straight a over denominator 3 straight b end fraction
rightwards double arrow square root of 2 space is space straight a space rational space number. space
left parenthesis space since space straight a comma space straight b space and space 3 space are space integers space rightwards double arrow fraction numerator straight a over denominator 3 straight b space end fraction space is space straight a space rational space number right parenthesis
This space contradicts space the space fact space that space square root of 2 space is space an space irrational space number.
So comma space our space assumption space was space wrong.
Hence comma space 3 square root of 2 space is space an space irrational space number. end style

Answered by Yasmeen Khan | 24th May, 2021, 01:22: PM