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

1 Answer
Feb 19, 2017

#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.