Question

My question is a complex numbers question: square root -6 times square root -24 the answer is -12, but I don't know how to solve it

Answer 1

see below

Explanation:

sqrt( -6) * sqrt(-24)

We know that sqrt(a b) = sqrt(a) sqrt(b)

sqrt(6) sqrt(-1) * sqrt(24) sqrt(-1)

We know that sqrt(-1) = i

sqrt(6) i * sqrt(24) i

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(6*24) i*i

sqrt(144) i^2

12 i^2

We know that i^2 = -1

12 (-1)

-12