What is the square root of -16 times the square root of -10?

1 Answer
Bill Jorgensen
May 19, 2018

-4sqrt(10)

Explanation:

By definition of imaginary numbers: i = sqrt(-1)

sqrt(-16) = 4*sqrt(-1) = 4i

sqrt(-10) = sqrt(10)*sqrt(-1) = sqrt(10)i

i^2=i*i= sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1

so:

4i * sqrt(10)i = 4sqrt(10)* i^2 = 4sqrt(10)* (-1) = -4sqrt(10)

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