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

##### 1 Answer

Oct 30, 2017

#### Explanation:

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

By convention, the principal square root of a negative number

#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#