Final answer:
The expression −−175 simplifies to -√(-175) in simplest radical form, represented by option D. This involves recognizing the imaginary unit, where the square root of a negative number is indicated with 'i'.
Step-by-step explanation:
The correct simplification of −−175 in simplest radical form is -√(-175), which corresponds to option D. In mathematics, we typically don't leave square roots with negative numbers as they are undefined in the real number system. However, for the sake of finding the simplest form, we use the concept of imaginary numbers where the square root of a negative number is expressed with 'i', the imaginary unit such that i² = -1.
To simplify −−175, we look for square factors of 175. Since 175 = 25 × 7 and 25 is a square number, we can write −−175 as −√(25 × 7 × -1) = -5−√7i. This uses the property that for any positive number 'a', √(-a) = √a × √(-1) = √a × i, where i is the imaginary unit.