Question

Examine, whether (2 + √2)² is rational or irrational.

Answer 1

(2 + √2)² 

= 2² + (√2)² + 2 x 2 x √2  [using identity, (a+b)² = a² + b² + 2ab]

= 4 +  2 + 4√2

= 6 + 4√2 

Here, 6 is a rational number but 4√2 is an irrational number.  Since, the sum of a rational and an irrational number is an irrational number, therefore, (2+ √2)² is an irrational number.