Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?(1 point)
The irrational number between 5 and 7 is 6 – √
To check which of the given numbers is irrational between 5 and 7, we need to determine if any of them can be expressed as a fraction (rational number) or if they are non-repeating decimals (irrational numbers).
The given numbers are:
- 6–√
- 12−−√
- 27−−√
- 36−−√
Let's calculate the square roots of these numbers to see if they are rational or irrational.
- The square root of 6 is approximately 2.449. This is an irrational number.
- The square root of 12 is approximately 3.464. This is an irrational number.
- The square root of 27 is approximately 5.196. This is an irrational number.
- The square root of 36 is 6, which is a rational number.
Based on these calculations, we can conclude that 6–√, 12−−√, and 27−−√ are all irrational numbers between 5 and 7.