Prove that square root of 5 is irrational.

Asked by roysubarna2016 | 17th Feb, 2019, 11:26: AM

Expert Answer:

let space square root of 5 space is space rational.... assumption
so comma
square root of 5 equals straight p over straight q.... straight p space and space straight q space are space co space prime
squaring
5 equals straight p squared over straight q squared
straight q squared cross times 5 equals straight p squared............. left parenthesis 1 right parenthesis
5 space divides space straight p squared
5 space divides space straight p
straight p equals 5 straight a.......... say
sub space in space left parenthesis 1 right parenthesis
straight q squared cross times 5 equals open parentheses 5 straight a close parentheses squared
straight q squared equals 5 open parentheses straight a close parentheses squared
5 space divides space straight q
so space 5 space divides space both space straight p space and space straight q
but space that space can apostrophe straight t space be space true space since space straight p space and space straight q space are space co space prime
so space assumption space is space wrong
square root of 5 space is space irrational

Answered by Arun | 17th Feb, 2019, 12:37: PM