Elaina, Miguel, and Swati are calculating the product of 6–√6 and 2323.

Question

Elaina says the answer is irrational because both numbers are irrational.

Miguel says the answer is rational because both numbers are rational.

Swati says the answer is irrational because one number is rational and the other number is irrational.

Who is correct? Enter the number that corresponds to the correct answer.

Elaina

Miguel

Swati

(1 point)

Answer 1

To determine who is correct, we need to analyze the nature of the numbers involved in the calculation.

The number \( 6 - \sqrt{6} \) is irrational because it involves the square root of an irrational number. On the other hand, \( 2323 \) is a rational number since it can be expressed as \( \frac{2323}{1} \).

The product of a rational number and an irrational number is always irrational. Therefore, when we multiply \( 6 - \sqrt{6} \) (irrational) by \( 2323 \) (rational), the result will be irrational.

Thus, the correct answer is Swati, who states that the answer is irrational because one number is rational and the other is irrational.

So, the correct response is:

Swati