Question

The product of a multiplication problem is 225−−−√ . What do you know about the factors?(1 point) Responses 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. At least one factor is irrational because the product is irrational. 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.

Answer 1

The product you mentioned, \(\sqrt{225}\), is actually equal to 15, which is a rational number.

Since the product (15) is rational, both factors can also be rational. In multiplication, if the product is rational, it is possible for both factors to be rational as well. However, it is also possible to have one rational factor and one irrational factor where the product is still rational (for example, \(r \cdot \sqrt{n}\) where \(r\) is rational and \(\sqrt{n}\) is irrational).

Given that \(\sqrt{225}\) is rational (15), the most accurate statement regarding the factors is:

They are both rational because the product is rational.