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

Question

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

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.

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

To analyze the factors of the product \( \sqrt{225} \):

1. Calculating \( \sqrt{225} \): \[ \sqrt{225} = 15 \] This result is a rational number.

2. Properties of Rational and Irrational Numbers:

   • The product of two rational numbers is rational.
   • The product of a rational number and an irrational number is irrational.
   • The product of two irrational numbers can be either rational or irrational.

Since \( \sqrt{225} \) results in 15, which is a rational number, both factors involved in obtaining this product could potentially be rational.

Given that the product is rational (15), we can conclude that both factors are rational, provided they are multiplied together to give a rational product.

Therefore, the correct response is: They are both rational because the product is rational.