Question

Would the product of two irrational elements always be irrational? Please justify or explain your response

Answer 1

Answer:

No

Step-by-step explanation:

Simple counterexample: $\sqrt{2}$ which is famously irrational. As the second number let’s take $2\sqrt{2}$ which obviously is also irrational. Their product is $\sqrt{2}\cdot 2\sqrt{2} = 2\cdot 2 = 4$ which is a rational number.