The product of a multiplication problem is 225−−−√ . What do you know about the factors?(1 point)

Question

Responses

It cannot be predicted based on the information given.
It cannot be predicted based on the information given.

One factor is rational, but the other is irrational.
One factor is rational, but the other is irrational.

They are both rational because the product is rational.
They are both rational because the product is rational.

At least one factor is irrational because the product is irrational.

Answer 1

The correct response is:

They are both rational because the product is rational.

Here's why: The square root of 225 is 15, which is a rational number. Therefore, if the product is 15, both factors must be rational. In a multiplication problem, if the product is rational, then it can be concluded that both factors must also be rational since the product of two irrational numbers could yield a rational product, but it isn't guaranteed. However, in this case, since the square root of 225 is a rational number (15), both factors can be considered rational.