Question
Micah and Sierra and Lexie are discussing the results of the sum of √8 + 3/2 Lexi says the results is irrational because one number is irrational and the other is rational Sophia says the answer is right now Mariah says the answers are irrational because both numbers are irrational who is correct Mariah Sophia or Lexi
Answers
GPT-4o mini
To determine who is correct, let's analyze the expression \( \sqrt{8} + \frac{3}{2} \).
1. **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.
2. **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.
1. **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.
2. **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.