Question

3. The operation is defined as follows: For any positive numbers a and b. a^ a b = sqrt(a + sqrt(b)) . Which of the following is an integer? a. 11 deg * 5 b. 4 ^ 9 c. 4 ^ 16 d. 7 otimes 4

Answer 1

Upon evaluating the options using the operation defined as a^ a b = sqrt(a + sqrt(b)), option d, assumed as 7 ^ 4, yields 3, which is an integer. Hence, option d is the correct answer.

Step-by-step explanation:

The question asks which of the given operations results in an integer, based on the operation defined as a^ a b = sqrt(a + sqrt(b)) for any positive numbers a and b. We must evaluate each option to determine if the result is an integer.

• Option a, 11 deg * 5, is not applicable as it seems to be a typo.
• Option b, 4 ^ 9, results in sqrt(4 + sqrt(9)) = sqrt(4 + 3) = sqrt(7), which is not an integer.
• Option c, 4 ^ 16, results in sqrt(4 + sqrt(16)) = sqrt(4 + 4) = sqrt(8), which is not an integer.
• Option d, 7 otimes 4, seems to be a typo, but assuming it means 7 ^ 4, we have sqrt(7 + sqrt(4)) = sqrt(7 + 2) = sqrt(9), which is 3, and it is an integer.

Therefore, the correct answer is option d, which in this context is assumed to mean 7 ^ 4, as it results in an integer when evaluated using the defined operation.