Question

Which expression is equivalent to √ -80?

Answer 1

Answer: Choice C

which is the expression 4*sqrt(5)*i,  where i = sqrt(-1)

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Explanation:

Factor -80 in such a way where we pull out -1 and we also factor out the largest perfect square possible. In this case, it would be 16 because 80 = 16*5. So this means -80 = -1*16*5 which leads to...

sqrt(-80) = sqrt(-1*16*5)

sqrt(-80) = sqrt(-1)*sqrt(16)*sqrt(5)

sqrt(-80) = i*4*sqrt(5)

sqrt(-80) = 4i*sqrt(5)

sqrt(-80) = 4*sqrt(5)*i