## Answer :

**Answer:**

To determine if (2 + √2)² is a rational number or not, let's first expand the expression:

(2 + √2)² = (2 + √2)(2 + √2)

= 2(2) + 2(√2) + 2(√2) + (√2)(√2)

= 4 + 2√2 + 2√2 + 2

= 6 + 4√2

Now, to determine whether this expression is rational or not, we need to see if it can be expressed as a ratio of two integers.

In this case, 6 is an integer, but 4√2 is not an integer because √2 is irrational.

Therefore, the expression (2 + √2)² = 6 + 4√2 is an irrational number, as it cannot be expressed as a ratio of two integers.