Which expression is equivalent to the square root of - 80?

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

Answer:C

Step-by-step explanation:

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