Question

Prove that 3-√5 is
irrational​

Answer 1

Letus assume that 3 + √5 is a rational number.

So it can be written in the form a/b

3 + √5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving

3 + √5 = a/b

we get,

=>√5 = a/b – 3

=>√5 = (a-3b)/b

=>√5 = (a-3b)/b

This shows (a-3b)/b is a rational number.

But we know that √5 is an irrational number, it is contradictsour to our assumption.

Our assumption 3 + √5 is a rational number is incorrect.

3 + √5 is an irrational number

Hence proved.