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CBSE Class 10 Answered

Prove that square root of 5 is irrational.
Asked by roysubarna2016 | 17 Feb, 2019, 11:26: AM
answered-by-expert 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 | 17 Feb, 2019, 12:37: PM
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