Question

Prove that  √3-2 is irrational​

Answer 1

prove :

Let 3-√2 is an rational number.. such that

3-√2 = a/b ,where a and b are integers and b is not equal to zero ..

therefore,

3 -√2 = a/b

√2 = a/b +3

√2 = (3b+a) /b

therefore, √2 = (3b +a)/b is rational as a, b and 3 are integers..

It means that √2 is rational....

But this contradicts the fact that √2 is irrational..

So, it concludes that 3-√2 is irrational..

hence proved..