A rational number and an irrational number are multiplied together. The product is a rational number. What type of rational number must the product be?(1 point)

Question

Responses

greater than 1
greater than 1
a perfect square
a perfect square
zero
zero
an integer

Answer 1

The product of a rational number and an irrational number is always irrational, unless the rational number is zero. In such a case, multiplying zero by any number (rational or irrational) results in zero, which is a rational number.

Therefore, if the product of a rational number and an irrational number is a rational number, that rational number must be zero.