Question

Prove that 1/3-2√5
is an irrational number.​

Answer 1

Answer:

We know 2√5 is irrational

let root 1/3 - 2√5 be of the form p/q where p and q are co prime and q is not equal to zero

1/3 - 2√5 = p/q

- 2√5 = p/q - 1/3

2√5 = 1/3 - p/q

2√5 = q - 3p / 3q

√5 = q - 3p/ 6q

Hence, √5 should be rational from the above eqn.

But we know that √5 is irrational

So, 1/3 - 2√5 is irrational