Question

prove that 6+2√5 is irrational​

Answer 1

Answer:

let us assume that it is rational and can be expressed in form a/b , where a and b are positive coprime and b≠0

then

a/b = 6 + 2✓5

2✓5 = a/b-6

✓5= a-6b/2b

now we can see that a-6b/2b is rational thus ✓5 must also be rational but this contradicts the fact that ✓5 is irrational thus our assumption fail and hence 6+2✓5 is irrational