Question

Give an example of each:(1)2 irrational number whose difference is rational. (2)2 irrational number whose product is rational. (3)2 irrational number whose quotient is rational. (4)2 irrational number whose sum is rational.

Answer 1

Dear Student,

$$\begin{gathered} \left(1\right).\mathrm{The}\mathrm{difference}\mathrm{of}\mathrm{the}\mathrm{irrational}\mathrm{numbers}\sqrt{2}\mathrm{and}\sqrt{2}\mathrm{is}\mathrm{zero},\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}. \\ \left(2\right).\mathrm{The}\mathrm{product}\mathrm{of}\mathrm{irrational}\mathrm{numbers}\sqrt{18}\mathrm{and}\sqrt{2}\mathrm{is}6,\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}. \\ \left(3\right).\mathrm{The}\mathrm{quotient}\mathrm{of}\mathrm{irrational}\mathrm{numbers}\sqrt{12}\mathrm{and}\sqrt{3}\mathrm{is}2,\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}. \\ \left(4\right).\mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{irrational}\mathrm{numbers}\sqrt{2}\mathrm{and}-\sqrt{2}\mathrm{is}\mathrm{zero},\mathrm{which}\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}. \end{gathered}$$
Regards