Question

Express the radical using the imaginary unit, i.

Express your answer in simplified form.
± s√ (-20) = ± ( )

Answer 1

To express ±√(-20) using the imaginary unit i, the expression simplifies to ± 2√(5) * i.

Step-by-step explanation:

To express the radical using the imaginary unit, i, you start by understanding that i is defined as i = √(-1). Therefore, when you have a negative number inside a square root, you can factor out the negative as an i. So √(-20) can be rewritten as √(20) * √(-1), which simplifies to √(20) * i.

Now, we simplify √(20) by finding the prime factors of 20, which are 2 * 2 * 5. We take out pairs of primes from under the radical as single numbers. Here, we take out a pair of 2s. This gives us 2√(5) * i. Finally, we can include ± to denote both the positive and negative possibilities, so the expression becomes ± 2√(5) * i.