Question

prove that √2-3√2 is irrational ​

Answer 1

Answer:

Suppose √3 - √2 is rational .

Let √3 - √2 = r       where r is a rational.

∴  (√3 - √2)2 = r2  

∴  2 + 3 - 2√6 = r2

∴√6 = (5 - r2 ) / 2

Now , LHS = √6 is an irrational number .

RHS =  (5 - r2 ) / 2  But rational number cannot be equal to an irrational.

∴our supposition is wrong.

∴ √3 - √2 is irrational

Step-by-step explanation: