Final answer:
To simplify √(-48)i, we express the square root of a negative number using the imaginary unit i, find the square root of 48, and then simplify the expression to get -4√(3).
Step-by-step explanation:
To simplify √(-48)i, we need to first simplify the square root of a negative number. To do this, we can use the property that √(-1) is equal to i, where i is the imaginary unit. Knowing this, we can write the expression as √(-48)i = √(48) * √(-1) * i.
Now, we simplify the square root of 48. We look for perfect square factors of 48, which are 16 and 3 (since 16 * 3 = 48 and 16 is a perfect square). So, we can write √(48) as √(16 * 3) = √(16) * √(3) = 4√(3).
Putting it all together, we have √(-48)i = 4√(3) * √(-1) * i = 4√(3) * i * i = 4√(3) * i². Since i² = -1, the expression simplifies to -4√(3).