To determine who is correct, let's analyze the expression \( \sqrt{8} + \frac{3}{2} \).
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Identify the types of numbers:
- \( \sqrt{8} \) is an irrational number because it cannot be expressed as a fraction of two integers.
- \( \frac{3}{2} \) is a rational number because it can be expressed as a fraction of two integers.
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Sum of a rational and an irrational number:
- The sum of a rational number and an irrational number is always irrational. So, \( \sqrt{8} + \frac{3}{2} \) will be irrational.
Now, let's evaluate the statements made by Micah, Sierra, Lexi, and Mariah:
- Lexi states the result is irrational because one number is irrational and the other is rational. This is correct.
- Sophia doesn't provide a complete rationale for her statement. Just saying the answer is "right" isn't enough to determine correctness.
- Mariah claims the answer is irrational because both numbers are irrational. This is incorrect because only \( \sqrt{8} \) is irrational, while \( \frac{3}{2} \) is rational.
Thus, Lexi is correct in stating that the result is irrational.
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