Question

Classify the following numbers as rational or irrational.
$(2+\sqrt{2})(2-\sqrt{2})$

Answer 1

$(2+\sqrt{2})(2-\sqrt{2})=\left[\right(2{)}^2-\left(\sqrt{2}{)}^2\right]$

=$(4-2)=2$

After simplification we get $(2+\sqrt{2})(2-\sqrt{2})=2$

The number 2 is a rational number then $(2+\sqrt{2})(2-\sqrt{2})$ is a rational number