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The product of a multiplication problem is √225 (radical symbol on top of the 225)

. 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.

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.

1 answer

To analyze the product of the multiplication problem, we first need to calculate \(\sqrt{225}\).

\[ \sqrt{225} = 15 \]

Since 15 is a rational number (it can be expressed as a fraction \(\frac{15}{1}\)), we can conclude that the product is rational.

Now, considering the factors in a multiplication problem that yields a rational product:

  1. If both factors are rational, their product is rational.
  2. If one factor is rational and the other is irrational, the product is irrational.
  3. If both factors are irrational, their product can be either rational or irrational.

Since we know that the product is a rational number (15), it indicates that both factors must also be rational numbers. Therefore, the correct response is:

They are both rational because the product is rational.