Final answer:
√7 is the only irrational number among the options, as it cannot be expressed as a fraction of two integers.
Step-by-step explanation:
The question asks which of the following is irrational: A) √4/√9, B) √12/√3, C) √7, D) √81. An irrational number is a number that cannot be expressed as a fraction of two integers. That is, its decimal form is non-terminating and non-repeating.
To determine which option is irrational, let's evaluate each one:
- √4/√9 = 2/3, which is a rational number.
- √12/√3 = √(12/3) = √4 = 2, which is also a rational number.
- √7 cannot be simplified to a fraction of integers, making it an irrational number.
- √81 = 9, and this is a rational number since it can be expressed as the fraction 9/1.
Therefore, the answer is C) √7, which is the only irrational number in the list provided.