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hich of the following is an irrational number between 4 and 8?%0D%0A%0D%0AShow your work. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A5–√%0D%0A5%0D%0Asquare root of 5%0D%0A%0D%0A8–√%0D%0A8%0D%0Asquare root of 8%0D%0A%0D%0A12−−√%0D%0A12%0D%0Asquare root of 12%0D%0A%0D%0A17−−√
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Answered by
GPT-4o mini
To determine which of the provided options is an irrational number between 4 and 8, let's analyze each choice:
1. **\(5\sqrt{}\)**: This seems to imply \( \sqrt{5} \). We will check its value:
- \( \sqrt{5} \approx 2.236\) (this is less than 4, so it does not meet the condition).
2. **5**: This is a rational number, as it can be expressed as \( \frac{5}{1} \).
3. **Square root of 5 (\( \sqrt{5} \))**: As calculated before, \( \sqrt{5} \approx 2.236\) (again this is less than 4, so it does not meet the condition).
4. **\(8\sqrt{}\)**: This seems to imply \( \sqrt{8} \). Let's find its value:
- \( \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \) (still less than 4).
5. **8**: This is also a rational number, as it can be expressed as \( \frac{8}{1} \).
6. **Square root of 8 (\( \sqrt{8} \))**: As calculated before, this is \( 2.828\), which is less than 4.
7. **\(12\sqrt{}\)**: This seems to imply \( \sqrt{12} \). Let's find its value:
- \( \sqrt{12} = 2\sqrt{3} \) and \( \sqrt{3} \approx 1.732\) so \( 2\sqrt{3} \approx 2 \times 1.732 = 3.464 \) (which is still less than 4).
8. **12**: This is a rational number, as it can also be expressed as \( \frac{12}{1} \).
9. **\(17\sqrt{}\)**: This seems to imply \( \sqrt{17} \). Let's find its value:
- \( \sqrt{17} \approx 4.123 \) (which is between 4 and 8 and is an irrational number).
So the only irrational number between 4 and 8 is **\( \sqrt{17} \)**.
1. **\(5\sqrt{}\)**: This seems to imply \( \sqrt{5} \). We will check its value:
- \( \sqrt{5} \approx 2.236\) (this is less than 4, so it does not meet the condition).
2. **5**: This is a rational number, as it can be expressed as \( \frac{5}{1} \).
3. **Square root of 5 (\( \sqrt{5} \))**: As calculated before, \( \sqrt{5} \approx 2.236\) (again this is less than 4, so it does not meet the condition).
4. **\(8\sqrt{}\)**: This seems to imply \( \sqrt{8} \). Let's find its value:
- \( \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \) (still less than 4).
5. **8**: This is also a rational number, as it can be expressed as \( \frac{8}{1} \).
6. **Square root of 8 (\( \sqrt{8} \))**: As calculated before, this is \( 2.828\), which is less than 4.
7. **\(12\sqrt{}\)**: This seems to imply \( \sqrt{12} \). Let's find its value:
- \( \sqrt{12} = 2\sqrt{3} \) and \( \sqrt{3} \approx 1.732\) so \( 2\sqrt{3} \approx 2 \times 1.732 = 3.464 \) (which is still less than 4).
8. **12**: This is a rational number, as it can also be expressed as \( \frac{12}{1} \).
9. **\(17\sqrt{}\)**: This seems to imply \( \sqrt{17} \). Let's find its value:
- \( \sqrt{17} \approx 4.123 \) (which is between 4 and 8 and is an irrational number).
So the only irrational number between 4 and 8 is **\( \sqrt{17} \)**.
Answered by
GPT-4o mini
Sure! Let's break it down step by step in simpler terms:
You want to find an irrational number (a number that can't be written as a simple fraction) that is between 4 and 8. Let's look at each option you provided:
1. **\( \sqrt{5} \)**: This is about 2.236, which is not between 4 and 8.
2. **5**: This is a whole number (5), so it is a rational number, but it is not between 4 and 8.
3. **\( \sqrt{8} \)**: This is about 2.828, which is also not between 4 and 8.
4. **\( \sqrt{12} \)**: This is about 3.464, which is still not between 4 and 8.
5. **12**: This is a whole number (12), so it is a rational number and not between 4 and 8.
6. **\( \sqrt{17} \)**: This is about 4.123, which is between 4 and 8, and it can't be written as a simple fraction, so it is irrational.
So the answer is **\( \sqrt{17} \)** because it is the only irrational number between 4 and 8!
You want to find an irrational number (a number that can't be written as a simple fraction) that is between 4 and 8. Let's look at each option you provided:
1. **\( \sqrt{5} \)**: This is about 2.236, which is not between 4 and 8.
2. **5**: This is a whole number (5), so it is a rational number, but it is not between 4 and 8.
3. **\( \sqrt{8} \)**: This is about 2.828, which is also not between 4 and 8.
4. **\( \sqrt{12} \)**: This is about 3.464, which is still not between 4 and 8.
5. **12**: This is a whole number (12), so it is a rational number and not between 4 and 8.
6. **\( \sqrt{17} \)**: This is about 4.123, which is between 4 and 8, and it can't be written as a simple fraction, so it is irrational.
So the answer is **\( \sqrt{17} \)** because it is the only irrational number between 4 and 8!
Answered by
GPT-4o mini
Sure!
1. **\( \sqrt{5} \)**: About 2.236 (not between 4 and 8).
2. **5**: Whole number (not between 4 and 8).
3. **\( \sqrt{8} \)**: About 2.828 (not between 4 and 8).
4. **\( \sqrt{12} \)**: About 3.464 (not between 4 and 8).
5. **12**: Whole number (not between 4 and 8).
6. **\( \sqrt{17} \)**: About 4.123 (between 4 and 8 and irrational).
**Answer: \( \sqrt{17} \)**.
1. **\( \sqrt{5} \)**: About 2.236 (not between 4 and 8).
2. **5**: Whole number (not between 4 and 8).
3. **\( \sqrt{8} \)**: About 2.828 (not between 4 and 8).
4. **\( \sqrt{12} \)**: About 3.464 (not between 4 and 8).
5. **12**: Whole number (not between 4 and 8).
6. **\( \sqrt{17} \)**: About 4.123 (between 4 and 8 and irrational).
**Answer: \( \sqrt{17} \)**.