Prove that 2root3/5 is irrational number 

Asked by Palarvind865 | 28th Jan, 2018, 11:34: PM

Expert Answer:

begin mathsize 16px style If space we space consider space fraction numerator 2 square root of 3 over denominator 5 end fraction space is space rational space number comma space we space can space write space it space in space the space form space of space straight p over straight q.
Hence comma
fraction numerator 2 square root of 3 over denominator 5 end fraction equals straight p over straight q
square root of 3 equals fraction numerator 5 straight p over denominator 2 straight q end fraction
As space space straight p over straight q space is space rational space number space then space fraction numerator 5 straight p over denominator 2 straight q end fraction space is space also space rational space number.
It space contradicts space to space square root of 3 space is space rational space number.
Hence comma space fraction numerator 2 square root of 3 over denominator 5 end fraction space is space irrational space number.
end style

Answered by Sneha shidid | 29th Jan, 2018, 09:53: AM