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

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Answer 1 · 2017-02-19T09:20:48

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

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

What is interesting here is what you must not do:

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

Note that for Real values of $a, b$ , the identity:

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

only holds when at least one of $a, b$ is non-negative.

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