the product of a multiplication problem is sqrt255. what do you know about the factors?

A. It cannot be predectied based on the information given.
B. one factor is rational, but the other is not
C. they are both rational because the product is rational.
D. At least one factor is irrational because the product is irrational

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

The product of the multiplication problem is \(\sqrt{255}\). To analyze the possible factors, we need to consider whether \(\sqrt{255}\) is a rational number or an irrational number.

Since \(255\) is not a perfect square, \(\sqrt{255}\) is an irrational number.

When we refer to multiplication: if the product of two numbers is irrational, at least one of the factors must also be irrational. This is because if both factors were rational, their product would also be rational.

Thus, the correct choice is:

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