Question

State True or False:

$(2-\sqrt{2})(2+\sqrt{2})$ is an irrational number.

• A. True
• B. False

Answer 1

The correct option is B False

$(2-\sqrt{2})(2+\sqrt{2})=4-2=2$.

Since. $2$ is an rational number, since its decimal representation is terminating .

Hence, $(2-\sqrt{2})(2+\sqrt{2})$ is a rational number.

Therefore, the given statement is false.