First, let's evaluate each person's statement regarding the product of \( \sqrt{6} \) and \( \frac{2}{3} \).
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Elaina's claim: She says the answer is irrational because both numbers are irrational.
- This claim is incorrect. While \( \sqrt{6} \) is irrational, \( \frac{2}{3} \) is a rational number. The product of a rational number and an irrational number is always irrational, but the reasoning she provides about both numbers being irrational is flawed.
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Miguel's claim: He says the answer is rational because both numbers are rational.
- This claim is incorrect because \( \sqrt{6} \) is not a rational number; it is irrational. Therefore, his conclusion that the product is rational is wrong.
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Swati's claim: She says the answer is irrational because one number is rational and the other number is irrational.
- This claim is correct. The product of \( \sqrt{6} \) (irrational) and \( \frac{2}{3} \) (rational) is indeed irrational.
Therefore, the correct person is Swati.
Enter the number that corresponds to the correct answer: 3