prove 1/root 2 is irrational no

Asked by jayasingh29march79 | 28th Jan, 2020, 07:05: AM

Expert Answer:

begin mathsize 16px style Let space us space assume space that space fraction numerator 1 over denominator square root of 2 end fraction space is space straight a space rational space number.
rightwards double arrow fraction numerator 1 over denominator square root of 2 end fraction equals space straight a over straight b space
rightwards double arrow space straight b over straight a space equals square root of 2 space
straight b over straight a space is space straight a space rational space number space rightwards double arrow square root of 2 space is space straight a space rational space number.
which space is space straight a space contradiction comma space means space our space assumption space was space wrong.
rightwards double arrow fraction numerator 1 over denominator square root of 2 end fraction space is space an space irrational space number. end style

Answered by Yasmeen Khan | 28th Jan, 2020, 11:14: AM