Final answer:
The square root of -77 is expressed using the imaginary unit as √77 * i, which is the simplified form of the radical expression.
Step-by-step explanation:
To express the radical square root of -77 using the imaginary unit, we first recognize that the square root of a negative number requires the use of imaginary numbers. The imaginary unit is denoted as i, where i is defined as the square root of -1. Therefore, to express the square root of -77, we separate it into the square root of 77 and the square root of -1.
The expression becomes √-77 = √77 * √-1. Since i is the square root of -1, we substitute i in place of √-1 and get √77 * i. The square root of 77 cannot be simplified further because 77 is not a perfect square. Thus, the simplified form is √77 * i or simply written as √77i.