Answer:

Given Expression:
The given expression is (3-√7)(3+√7).

Expanding the Expression:
To determine if the expression is rational or irrational, let's first expand it using the formula (a-b)(a+b) = a^2 - b^2.
So, (3-√7)(3+√7) = 3^2 - (√7)^2 = 9 - 7 = 2.

Analysis:
The result of the expression is 2, which is an integer. To determine if the number is rational or irrational, we need to understand the definitions of these terms.

Rational Numbers:
Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero.

Irrational Numbers:
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They are non-terminating and non-repeating decimals.

Conclusion:
Since the result of the expression (3-√7)(3+√7) is 2, which is an integer, we can conclude that the number is rational. This is because the number can be expressed as a ratio of two integers, 2/1. Therefore, the given expression is a rational number.