Question

Write any two irrational numbers such that:
1)Sum is rational
2) Sum is irrational
3) Difference is rational
4) Quotient is rational
5) Quotient is irrational

Answer 1

$$\begin{gathered} \left(1\right)\mathrm{Sum}\mathrm{is}\mathrm{rational} \\ \mathrm{Numbers}\mathrm{are}\sqrt{2}\mathrm{and}-\sqrt{2}\mathrm{as},\sqrt{2}+\left(-\sqrt{2}\right)=0,\mathrm{a}\mathrm{rational}\mathrm{number} \\ \left(2\right)\mathrm{Sum}\mathrm{is}\mathrm{irrational}. \\ \mathrm{Numbers}\mathrm{are}2\sqrt{3}\mathrm{and}\sqrt{3}\mathrm{as}2\sqrt{3}+\sqrt{3}=3\sqrt{3},\mathrm{an}\mathrm{irrational}\mathrm{number}. \\ \left(3\right)\mathrm{Difference}\mathrm{is}\mathrm{rational} \\ \mathrm{Numbers}\mathrm{are}\sqrt{5}\mathrm{and}\sqrt{5}\mathrm{as}\sqrt{5}-\sqrt{5}=0 \\ \left(4\right)\mathrm{Quotient}\mathrm{is}\mathrm{rational}. \\ \mathrm{Numbers}\mathrm{are}2\sqrt{3}\mathrm{and}\sqrt{3}\mathrm{as}\frac{2\sqrt{3}}{\sqrt{3}}=2,\mathrm{a}\mathrm{rational}\mathrm{number}. \\ \left(5\right)\mathrm{Quotient}\mathrm{is}\mathrm{irrational} \\ \mathrm{Numbers}\mathrm{are}\sqrt{6}\mathrm{and}\sqrt{3}\mathrm{as}\frac{\sqrt{6}}{\sqrt{3}}=\sqrt{2},\mathrm{an}\mathrm{irrational}\mathrm{number}. \end{gathered}$$