Question

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

Answer 1

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

Explanation:

`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.