Question

prove that√5 is a irrational number​

Answer 1

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Answer 2

Answer:

let root 5 a rational numbers can written in form of p/ q and where p Andy are co primes.

root 5 = p/ q

square both side

5 = p square / q square

q square = p square / 5

if p square is divisible by 5 then p is also divisible by 5 according to theorem (equation 1 )

now let , p square = 5c square

q square =( 5c) square / 5

q square = 25c square / 5

q square = 5 c square

c square = q square / 5

if q square is divisible by 5 the it is also divisible by q ( equation 2)

by equation 1 and I 2 :

we observed that there is a contradiction that p and q are not co primes becoz they are divisible by 5 this contradiction arose due to our wrong assumption that root 5 is rational

hence root 5 is irrational

Co primes : numbers having common factor 1 not any other

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