Question

question 6 of 10
which choice is equivalent to the expression below?
\sqrt{-64}

a. -8

b. 64i

c. 8 + i

d. -64

e. 8i

Explanation:

Step1: Recall the imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \).

Step2: Simplify the square root

We can rewrite \( \sqrt{-64} \) as \( \sqrt{64 \times (-1)} \).
Using the property of square roots \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (for \( a\geq0, b\geq0 \), and extended to complex numbers), we have:
\( \sqrt{64 \times (-1)} = \sqrt{64} \times \sqrt{-1} \)
Since \( \sqrt{64} = 8 \) and \( \sqrt{-1} = i \), this simplifies to \( 8i \).

Answer:

E. \( 8i \)