Question

If x and y are irrational numbers, then xy is also an irrational number. Give an example that disproves the statement.

Answer 1

let x and y be irrational number.

then, take

`x=\sqrt[]{5\text{ }}and\text{ y=}\sqrt[]{5}`

therefore,

`\begin{gathered} xy=\sqrt[]{5}*\sqrt[]{5} \\ =5 \end{gathered}`

5 is a rational number.

we have disproved the given statement.