Question

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

Answer 1

`-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)`