Simon, Asia, and Jiovanni are finding the product of a rational and irrational number.

Question

Simon says the result should be irrational because the product of an irrational and rational number is always irrational.

Asia says the result should be zero because the product of an irrational and rational number is always zero.

Jiovanni says the result should be rational because the product of an irrational and rational number is always rational.

Who is correct?

(1 point)
Responses

Asia
Asia

Simon
Simon

None of them are correct.
None of them are correct.

Jiovanni

Answer 1

Simon is correct.

The product of a non-zero rational number and an irrational number is always irrational. Asia's statement is incorrect because the product does not have to be zero unless the rational number is zero. Jiovanni's statement is also incorrect because the product of an irrational and a non-zero rational number is not rational.

So, the correct answer is Simon.