Question

Prove 3-5√2 is irration​

Answer 1

Answer:

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

So it can be written in the form a/b

3 - 5√2 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 - 5√2 = a/b we get,

=>5√2 = a/b + 3

=>5√2 = (a+3b)/b

=>√2= (a+3b)/5b

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

so it contradictory assumption.

Our assumption of 3 -5√2 is a rational number is incorrect.

3 -5√2 is an irrational number

Hence proved...…..