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let us assume tht √5 is rational

so v can get a/b such tht - √5=a/b

⇒√5b=a ..................... (i)

squaring on both sides v get

5b²=a² ............(ii)

so 5 divides a² which v can say as 5 divides a

now, let a=5c for some integer c.

now again by squaring on both sides v get

a²=25c² ........................(iii)

now by (ii)

substituting a²

v get

5b²=25c²

i.e , b²=5c²

⇒5 divides c² which v can say tht 5 divides c.

so v can say tht a and b have 5 as a common factor.

but this contradicts d fact tht a and b r co prime( they do not have any other factor other than 1)

this contradiction arises due to our wrong consumption tht √5 is rational

hence v can conclude tht √5 is irrational.

hope it helped u!!!!!