The product of a multiplication problem is 225−−−√

Question

. What do you know about the factors?(1 point)
Responses

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

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

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

It cannot be predicted based on the information given.

Answer 1

The square root of 225 is \( \sqrt{225} = 15 \), which is a rational number. Therefore, the product is rational.

Based on the properties of multiplication:

• If both factors were rational, the product would also be rational.
• If one factor is irrational, then the product can still be rational if the other factor is a specific rational number that cancels out the irrational part (for example, multiplying by its conjugate).

However, since \( \sqrt{225} \) is rational (equal to 15), this indicates that both factors could likely be rational.

Given this, the correct response is:

They are both rational because the product is rational.