To determine which of the given options is an irrational number between 5 and 7, we can evaluate each square root:
-
√6: This is approximately 2.45 (since \(2.45^2 \approx 6\)), which is not between 5 and 7.
-
√12: This is approximately 3.46 (since \(3.46^2 \approx 12\)), which is also not between 5 and 7.
-
√27: This is approximately 5.2 (since \(5.2^2 \approx 27\)), which falls between 5 and 7. Additionally, √27 can be simplified to \(3√3\) (since \(27 = 9 \times 3\)), and \(3√3\) is also irrational.
-
√36: This is equal to 6, which is a rational number and falls between 5 and 7.
Among these, the only irrational number between 5 and 7 is √27.
11 answers