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

Question

. 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.

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.
It cannot be predicted based on the information given.

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

Answer 1

To determine the nature of the factors in the multiplication problem where the product is \( \sqrt{225} \), we first simplify the product:

\[ \sqrt{225} = 15 \]

The number 15 is a rational number. When considering the factors of a rational number, we can conclude:

1. Both factors can be rational. For example, \( 1 \times 15 = 15 \) and both 1 and 15 are rational.
2. One factor can be irrational while the other is rational. For example, \( \sqrt{2} \times 7.5 = 15 \), where \( \sqrt{2} \) is irrational and \( 7.5 \) is rational.

However, in the case of the product being 15 (a rational number), it is also possible that both factors could be rational.

Thus, the best conclusion is:

They are both rational because the product is rational.