Question

Examine, whether the following number are rational or irrational:

`(2-sqrt2)(2+sqrt2)`

Answer 1

Let `x=(2-sqrt2)(2+sqrt2)`

`rArrx=(2)^2-(sqrt2)^2`          {As (a + b)(a - b) = a² - b²}

⇒ x = 4 - 2

⇒ x = 2

So `(2-sqrt2)(2+sqrt2)` is a rational number