Question

3+2 route 5 irrational prove that​

Answer 1

Answer:

Given:3 + 2√5

To prove:3 + 2√5 is an irrational number.

Proof:

Let, us assume that 3 + 2√5 is a rational number.

So, it can be written in the form a/b

3 + 2√5 = a/b

Here a and b are co prime numbers and b ≠ 0

Solving 3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

so it contradictsour assumption.

Our assumption of3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved