Which of the following is an irrational number between 5 and 7:

Question

√
6
, 
√
12
, 
√
27
, 
√
36
?(1 point)

Answer 1

To determine which of the given options is an irrational number between 5 and 7, we'll evaluate each of the square roots:

1. √6: The square root of 6 is approximately 2.45, which is not between 5 and 7.
2. √12: The square root of 12 is approximately 3.46, which is also not between 5 and 7.
3. √27: The square root of 27 is approximately 5.2, which is between 5 and 7 and is an irrational number.
4. √36: The square root of 36 is exactly 6, which is rational and is between 5 and 7.

Thus, the only irrational number between 5 and 7 among the options provided is √27.