To determine which of the given options is an irrational number between 5 and 7, we can evaluate each square root:
- √6: Approximately equal to 2.45. This is not between 5 and 7.
- √12: Simplifies to √(4 * 3) = 2√3. Since √3 is approximately 1.73, we have 2√3 ≈ 3.46. This is also not between 5 and 7.
- √27: Simplifies to √(9 * 3) = 3√3. Therefore, 3 * 1.73 ≈ 5.19, which is between 5 and 7 and is an irrational number.
- √36: Equal to 6, which is a rational number but does fall between 5 and 7.
Thus, the irrational number between 5 and 7 from the choices is √27.