Question

prove that √5 is irrational ​

Answer 1

Answer:

Step-by-step explanation:

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are intezers.

so, √5 = p/q

p = √5q

we know that 'p' is a rational number. so √5 q must be rational since it equals to p

but it doesnt occurs with √5 since its not an intezer

therefore, p =/= √5q

this contradicts the fact that √5 is an irrational number

hence our assumption is wrong and √5 is an irrational number.

Answer 2

Answer:

let us assume that root 5 is rational we can find integers a and b does not equals to zero such that root 5=a/b

where is a and b have common factor other than one that we can divide by the common factor and assume that A and B are coprime so root 5 equals to a squaring both side we get 5B square equals to a square a square is divisible by 5 and is also divisible by 5 we can write equals to 5c

for some integer c substituting for a we get 5b square equals to 25 c square that is is b square equals to 5 c square that means b square is divisible by 5 and b is also divisible by 5 a and b at least 5 Common Factor so a and b are coprime and our contradiction has arisen wrong because of our incorrect assumption that root 5 is is rational so we conclude that root 5 is irrational....THANKYOU I HOPE YOU WILL UNDERSTOOD