Prove 1/ Root over 11 is an irrational number

Asked by bhattacharyapriyanjana49 | 7th Apr, 2022, 08:43: PM

Expert Answer:

Suppose 1/sqrt{11} is rational
rightwards double arrow fraction numerator 1 over denominator square root of 11 end fraction equals straight p over straight q
rightwards double arrow straight q over straight p equals square root of 11
As space straight q over straight p space is space rational
Therefore comma space square root of 11 space is space rational.
This space is space straight a space contradiction space since space square root of 11 space is space irrational
Hence comma space fraction numerator 1 over denominator square root of 11 end fraction space is space irrational

Answered by Renu Varma | 8th Apr, 2022, 09:15: PM