Final answer:
The smallest subset containing the square root of 121 is the single-element set {11}, because 11 squared equals 121 and, typically, the non-negative square root is the principal square root considered.
Step-by-step explanation:
The smallest subset containing the square root of 121 is {11}.
The square root of a number is the value that, when multiplied by itself, gives the original number. For the number 121, the square root is 11, because 11 × 11 equals 121. Even though −11 is also a square root of 121, the question asks for the smallest subset; therefore, option b) {11} is the smallest subset containing a square root of 121, as it consists of only one element which is the non-negative square root.
In general, when referring to 'the square root' in mathematics, we often mean the principal (non-negative) square root, especially when addressing which subset would be minimal and relevant for a given situation.
The smallest subset containing the square root of 121 is option a) {-11, 11}.To find the square root of 121, we take the positive and negative square roots of 121, which are 11 and -11 respectively. Thus, the smallest subset that contains the square root of 121 is {-11, 11}.