High School

Which choice is equivalent to the expression below?

\(\sqrt{-125}\)

A. \(\sqrt{16}\)
B. \(16\sqrt{2}\)
C. \(3\)
D. \(2\sqrt{2}\)

Answer :

The expression √(-125) is equivalent to 5√5 \cdot i, where i is the imaginary unit. None of the provided choices (A, B, C, D) is an exact match.

The expression √(-125) involves finding the square root of a negative number, which is represented by an imaginary unit i. Here's the explanation:

1. √(-125) = √(125 * -1): Rewrite -125 as the product of 125 and -1.

2. √(125 * -1) = √125 * √(-1): Split the square root of the product into the product of square roots.

3. \(√125 * √(-1) = 5√5 * i\): Evaluate the square root of 125, which is 5√5, and introduce the imaginary unit i for the square root of -1.

So, the equivalent expression is 5√5 * i. None of the given choices
(A, B, C, D) directly matches this expression.