Final answer:
The simplified form of ( √-256 ) is 16i, as the square root of -256 involves multiplying the square root of 256, which is 16, by the imaginary unit 'i'. If a real number is expected, the answer is Ø because the square root of a negative number is not a real number.
Step-by-step explanation:
To simplify the expression ( √-256 ), we need to understand that the square root of a negative number involves the imaginary unit i, where i is defined as the square root of -1. Since 256 is a perfect square, being 16 squared (16² = 256), the square root of 256 is 16. Consequently, the square root of -256 is 16 times the imaginary unit i, or 16i.
Therefore, the simplified form of ( √-256 ) is 16i. If we were expecting a real number, the answer would be Ø as there is no real number whose square equals -256.