How do you simplify $sqrt(-3)sqrt(-12)$ ?

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Answer 1 · 2017-10-30T18:48:42

$sqrt(-3)sqrt(-12) = -6$

What is interesting about this example is that it is a counterexample to the often quoted "identity":

$sqrt(a)sqrt(b) = sqrt(ab)$

In fact this identity only holds if at least one of $a$ or $b$ is non-negative.

By convention, the principal square root of a negative number $n$ is given by:

$sqrt(n) = isqrt(-n)$

So:

$sqrt(-3)sqrt(-12) = i sqrt(3) * i sqrt(12) = i^2sqrt(3)sqrt(12) = -1 * sqrt(3 * 12) = -sqrt(36) = -6$

How do you simplify sqrt(-3)sqrt(-12)sqrt(-3)sqrt(-12)?