Question

Elaina, Miguel, and Swati are calculating the product of 6–√
and 23
.

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)
Person #
is correct.

Answer 1

Let's break down the statements and reasoning of Elaina, Miguel, and Swati regarding the product of \( \sqrt{6} \) (which is irrational) and 23 (which is rational).

1. **Elaina's Statement**: She says the answer is irrational because both numbers are irrational. This is **incorrect** because only one of the numbers (specifically \( \sqrt{6} \)) is irrational, while 23 is rational.

2. **Miguel's Statement**: He claims the answer is rational because both numbers are rational. This is **incorrect** as well since \( \sqrt{6} \) is irrational, and Miguel is mistaken that both numbers are rational.

3. **Swati's Statement**: She states that the answer is irrational because one number is rational and the other is irrational. This is **correct**. The product of any rational number (like 23) and an irrational number (like \( \sqrt{6} \)) is always irrational.

Therefore, the correct answer is:

**Swati is correct.**

So, you would enter the number that corresponds to Swati, which is:

**3** (assuming Elaina is 1, Miguel is 2, and Swati is 3)