prove that root of a+b is irrational.

Asked by rajani.vinod | 14th Jun, 2019, 10:03: PM

Expert Answer:

let space square root of straight a plus straight b end root space rational space
so
square root of straight a plus straight b end root equals straight p over straight q comma space straight p space and space straight q space are space co minus prime
also space consider space straight a plus straight b equals straight c
squaring
open parentheses straight c close parentheses equals straight p squared over straight q squared
cq squared equals straight p squared
straight c space divides space straight p squared
straight c space divides space straight p
let space straight p space equals space kc
now
cq squared equals straight p squared
cq squared equals straight k squared straight c squared
straight q squared equals straight k squared straight c
straight c space divides space straight q squared
straight c space divides space straight q
so space straight c space divides space both space straight p space and space straight q comma space which space is space not space possible space since space they space are space co space prime
so space our space assumption space is space wrong
square root of straight a plus straight b end root space is space irrational space

Answered by Arun | 16th Jun, 2019, 12:19: PM

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