Final answer:
The correct simplification of the given expression, assuming it is √12 + 6 × (-78 - 2), leads to -480 + 2√3, which does not match any of the provided answer choices. The answer is 'None of the above.'
Step-by-step explanation:
The student is asking for help in distributing and simplifying an expression involving square roots and multiplication. The expression provided in the question seems to contain a typo or may be incomplete. However, assuming the correct expression is the square root of 12 plus 6 multiplied by the quantity of -78 minus 2, we can proceed with the simplification as follows.
Firstly, we simplify the square root of 12.
√12 = √(4 × 3) = √4 × √3 = 2√3
Now, we multiply 6 by the sum of -78 and -2.
6 × (-78 - 2) = 6 × -80 = -480
Adding 2√3 to -480 does not simplify to any of the options given A, B, C, or D. Therefore, the answer is None of the above. Remember to always double-check your work to ensure the answer is reasonable.