Question

Prove that 1 - root 5 is irrayional

Answer 1

Given

• 1-√5 is a no
• √5 is irrational

To prove

• it is irrational no

Proof

Let 1-√5 be a rational no

Then they must be exsist in the form of a/b

Therefore

1-√5 = a/b

=>1-a/b =√5

=>(b-a)/b =√5

Here (b-a)/b is rational

So √5 also be rational

• But it is given that √5 is irrational no

From this we can say that our assumption is wrong that 1-√5 is rational .

Hence 1-√5 is a irrational no