Which of the following is equal to sqrt(-4)?
Check the final answer first, then review the worked steps.
Problem
Which of the following is equal to sqrt(-4)?
Answer
2i
Step-by-step solution
- Understand the imaginary unit: The imaginary unit, denoted by $i$, is defined as the square root of -1. That is, $i = \sqrt{-1}$.
- Rewrite the expression: The expression $\sqrt{-4}$ can be rewritten using the properties of square roots. We can separate the negative sign from the number 4: $\sqrt{-4} = \sqrt{4 \times -1}$.
- Apply the product property of square roots: The product property of square roots states that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$. Applying this to our expression, we get: $\sqrt{4 \times -1} = \sqrt{4} \times \sqrt{-1}$.
- Calculate the square roots: We know that $\sqrt{4} = 2$ and, by definition, $\sqrt{-1} = i$. Substituting these values, we have: $2 \times i = 2i$.
- Identify the correct option: Comparing our result with the given options, we find that $2i$ is one of the choices.