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

Question

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

To determine who is correct, we need to analyze the numbers involved:

• \( 6 - \sqrt{6} \) is irrational since it involves the square root of 6 (an irrational number). The difference between a rational number (6) and an irrational number (\(\sqrt{6}\)) is also irrational.
• \( 23 \) is a rational number.

Now, let's calculate the product:

Since one number ( \( 6 - \sqrt{6} \) ) is irrational and the other number ( \( 23 \) ) is rational, the product of a rational number and an irrational number is always irrational.

Thus, Swati's statement that the product is irrational because one number is rational and the other is irrational is correct.

So the answer is:

Swati is correct.