Question

prove that root 5 is irrational

Answer 1

let root 5 be a rational no.
√5 =a /b
squaring both sides,
5=a ka square /b ka square
5b ka square =a ka square. ------equation 1
b ka square =a square /5
a square is divisible by 5
so, a is also divisible by 5
let a=5c
put a=5c in equation 1

5b ka square =5c ka while square
5b ka square =25 c ka square

b square =5 c ka square
b square /5 =c square
b square is divisible by 5
so , a is also divisible by 5
a and b have atleast 5 as a common factor .this condicts the fact that a and b are co -prime numbers . so, our assumption is wrong.
hence,root 5 is an irrational number.