can the product of two irrational numbers be rational? explain your answer and support with an example.

Brief Explanations:

Irrational numbers are non - repeating, non - terminating decimals. But when some irrational numbers are multiplied, the non - rational parts can cancel out. For example, consider $\sqrt{2}$ and $\sqrt{8}$. $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$. Then $\sqrt{2}\times\sqrt{8}=\sqrt{2}\times2\sqrt{2}=2\times2 = 4$, which is rational.

Answer:

Yes, the product of two irrational numbers can be rational. For example, $\sqrt{2}$ and $\sqrt{8}$ are irrational, and $\sqrt{2}\times\sqrt{8} = 4$ (a rational number).