Answer:
sqrt(-80) = 4sqrt(5)i
Step-by-step explanation:
Likely a list of answers should be provided. There are all kinds of possible answers (well 2 perhaps).
Begin by factoring 80 into prime factors.
80: 2*2*2*2*5
For ever pair of 2s, one can be taken outside the square root sign. The other one just disappears.
sqrt(80) = sqrt(2 * 2 * 2 * 2 * 5)
For every pair 2 is taken out of the root sign and the other forgotten
sqrt(2 * 2 * 2 * 2 * 5) = 2 * 2 * sqrt(5) = 4 sqrt(5)
The sqrt(-80) = 4sqrt(5)*sqrt(-1)
There is no real number that can be written as the sqrt(-1). So a number has been defined into existence. sqrt(-1) = i It's a definition, not a real number.
So the end result is sqrt(-80) = 4sqrt(5)i
