Final answer:
A) 3, 0.2, no real root. The real fourth root of 81 is 3; of 0.0016 it is 0.2. The number -625 doesn't have a real fourth root because it's a negative number and real roots are not defined for negatives in this context.
Step-by-step explanation:
Let's find the real fourth roots of the given numbers step by step.
To find the fourth root of 81, we can take the square root twice. The square root of 81 is 9, and then taking the square root of 9, we get 3. So, the fourth root of 81 is 3.
For the number 0.0016: its fourth root can also be found by taking square roots twice. The square root of 0.0016 is 0.04, and the square root of 0.04 is 0.2. Thus, the fourth root of 0.0016 is 0.2.
Since real roots of negative numbers are not defined in the set of real numbers, there's no real fourth root for -625. Hence, -625 has no real fourth root.
Combining all the answers, we find that the real fourth roots are 3, 0.2, and there's no real root for -625. So the correct option from the given choices would be A) 3, 0.2, no real root.