Simplify the number using the imaginary unit I. √(-28)

Question

Simplify the number using the imaginary unit I.


`√(-28)`

Answer 1

`2i√(7)`

Explanation:

Find factors of 28 that have a perfect square root. 28, 14, 7, 4, 2, 1. The factors that fit are 7 & 4 because 4 is the perfect square of 2.

For any positive number a,
`√(-a) = √(-1 * a) = √(-1) * √(a) = i√(a)`

`√(-28) = √(-4 * 7) = √(-4) * √(7) = 2i * √(7) =`
`2i√(7)`

Answer 2

2i√7 that is your answer