Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−
The irrational numbers between 5 and 7 are:
6–√ = 6 - √2 (approximately 4.59)
12−−√ = 12 - √5 (approximately 8.76)
27−−√ = 27 - √6 (approximately 20.80)
36−−√ = 36 - √7 (approximately 28.81)
So, all of the given options are irrational numbers between 5 and 7.
To determine which of the given numbers is an irrational number between 5 and 7, we can evaluate each option.
1. 6–√:
- The value of 6–√ is approximately 4.83, which is smaller than 5. Therefore, 6–√ is not between 5 and 7.
2. 12−−√:
- The value of 12−−√ is approximately 3.46, which is also smaller than 5. Therefore, 12−−√ is not between 5 and 7.
3. 27−−√:
- The value of 27−−√ is approximately 5.20, which is between 5 and 7. Therefore, 27−−√ is an irrational number between 5 and 7.
4. 36−:
- This option seems to be incomplete or truncated. Therefore, we cannot evaluate it as an irrational number between 5 and 7.
Thus, the only option that is an irrational number between 5 and 7 is 27−−√.