Question

prove root 5 irrational......... please urgent

Answer 1

Hope this will help you...
It's in pic....

Answer 2

Let us assume on the contrary that √5 is rational. So there exists two co prime positive integers a and b.

So, √5=a/b
√5b= a

Squaring on both sides
5b^2 =a^2
So a divides 5b^2 -----------》1

a=5c for some integer c.
Squaring on both sides,

a^2 =25c^2
Substituting a^2 value

5b^2=25c^2
b^2=5c^2 ------------》2

So b divides 5c^2.

So from 1 and 2 our assumption is wrong.Since we assumed that the two integers a and b has only a common factor 1. So √5 is irrational.