Final answer:
The irrational number among the options is C. √11, because it cannot be expressed as a simple fraction or a repeating or terminating decimal.
Step-by-step explanation:
The question asks us to identify the irrational number among the given choices: A. -4, B. 2/9, C. √11, and D. 8.26(repeating). An irrational number is a number that cannot be expressed as a simple fraction or a repeating or terminating decimal. Option A, -4, is an integer and hence rational. Option B, 2/9, is a simple fraction, also rational. Option D, 8.26(repeating), is a repeating decimal, which is also rational.
The correct answer is option C, √11, because the square root of 11 cannot be expressed as a simple fraction or a repeating or terminating decimal. Therefore, √11 is an irrational number. So, when we mention the correct option in the final answer, it is C. √11.