Question

sunny states that the product of two irrational numbers is always irrational.

which statement correctly describes whether sunny is correct or incorrect?

sunny is incorrect; the product of two irrational numbers may be either rational or irrational.
sunny is incorrect; the product of two irrational numbers is always rational.
sunny is correct; the product of two irrational number is always irrational.

Explanation:

Step1: Analyze the claim

Sunny claims the product of two irrational numbers is always irrational.

Step2: Find a counterexample

Multiply \(\sqrt{2}\) by \(\sqrt{2}\) to get \(2\), which is rational.

Step3: Find an supporting example

Multiply \(\sqrt{2}\) by \(\sqrt{3}\) to get \(\sqrt{6}\), which is irrational.

Step4: Formulate the conclusion

The product can be either rational or irrational, making Sunny incorrect.

Answer:

Sunny is incorrect; the product of two irrational numbers may be either rational or irrational.