Question

↵what happens to irrational number when multiplied,added or subtracted from a rational number or visversa?

Answer 1

When an irrational number is multiplied, added or subtracted from a rational number we get an irrational number.
$$\begin{gathered} \mathrm{Ex}:2\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}\mathrm{and}\sqrt{3}\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number}. \\ 2\times \sqrt{3}=2\sqrt{3},\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \\ 2+\sqrt{3}=2+\sqrt{3},\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \\ 2-\sqrt{3}=2-\sqrt{3},\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \end{gathered}$$


When a rational number is multiplied, added or subtracted from an irrational number we get an irrational number.
$$\begin{gathered} \mathrm{Ex}:2\mathrm{is}\mathrm{a}\mathrm{rational}\mathrm{number}\mathrm{and}\sqrt{5}\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number}. \\ \sqrt{5}\times 2=2\sqrt{5},\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \\ \sqrt{5}+2=\sqrt{5}+2,\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \\ \sqrt{5}-2=\sqrt{5}-2,\mathrm{is}\mathrm{an}\mathrm{irrational}\mathrm{number} \end{gathered}$$