## Elementary Algebra

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.