Answer
True
Work Step by Step
We mutiply $(2-\sqrt 7)(2+\sqrt 7)$ using the rule $(a+b)(a-b)=a^{2}-b^{2}$ to see if the product is a rational number or not:
$(2-\sqrt 7)(2+\sqrt 7)$
$=2^{2}-(\sqrt 7)^{2}$
$=4-7$
$=-3$
$-3$ is a part of the subset of rational numbers. Therefore, the product of $(2-\sqrt 7)(2+\sqrt 7)$ is indeed a rational number, and the statement is true.
