Question

Prove that 3-√5 is a irrational number

Answer 1

Step-by-step explanation:

let us assume that 3+2root5 is rational

so, 3+2root5=a/b ,where a and b are co-prime and b is not equal to zero

now,

3+2root5=a/b

or, 2root5=a/b-3

or, root5=a/2b - 3/2

since a and b  are integers we get a/2b - 3/2 as a rational

so, root5 is also rational.

but this contradicts the fact that root5 is irrational

this contradiction have arisen because of our incorrect assumption that 3+2root5 is rational

therefore, 3+2root5 is irrational