Final Answer:
The value of 12 + square root of -63 is 12 + 3i sqrt(7) (Option A).
Step-by-step explanation:
To find the value of 12 + square root of -63, we need to determine the square root of -63 and then combine it with 12. The square root of -63 can be expressed as 3i sqrt(7), where i is the imaginary unit. Thus, the result is 12 + 3i sqrt(7). This form represents the sum of a real number (12) and an imaginary number (3i sqrt(7)) (Option A).
Understanding complex numbers involves recognizing the imaginary unit i, where i² = -1. In this case, the square root of -63 introduces the imaginary component 3i sqrt(7), and combining it with the real part 12 yields the final expression 12 + 3i sqrt(7).
In conclusion, option A, 12 + 3i sqrt(7), accurately represents the value of 12 + square root of -63. The solution involves understanding the concept of imaginary numbers and the square root of negative values, resulting in a complex number with both real and imaginary components.