Question

Prove that 3+2√5 is irrational.​

Answer 1

Answer:

beacuse √5 is not a rational number

√5 =2.23606

Answer 2

Let us assume to the contrary that 3+2√5 is rational.

let 3+2√5=a/b( a and b are co-prime and positive integer

3+2√5= a/b

2√5= a/b-3

√5= 1/2(a/b-3)

√5= a/2b-3/2

Since a and b are integers

therefore a/2b-3/2 is a rational number.

therefore √5 is rational number

But √5 is an irrational number

This shows that our assumption that 3+2√5 is rational is false.

Therefore 3+2√5 is irrational.

Hope it helps you.........!!♥️