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

Jiovanni
Jiovanni

Simon
Simon

Asia
Asia

None of them are correct.

Answer 1

Simon is correct. The product of a non-zero rational number and an irrational number is always irrational.

Asia's claim that the product is always zero is incorrect; the product will only be zero if the rational number is zero.

Jiovanni's claim that the product is always rational is also incorrect because the product will be irrational if the rational number is non-zero.

Therefore, the correct response would be Simon.