Why is #sqrt(-2) sqrt(-3) != sqrt((-2) * (-3))# ?

1 Answer
Jan 9, 2017

Answer:

The "rule" #sqrt(ab) = sqrt(a)sqrt(b)# does not hold all of the time - especially when it comes to negative or complex numbers.

Explanation:

Here's another example:

#1 = sqrt(1) = sqrt((-1)*(-1)) != sqrt(-1)*sqrt(-1) = -1#

This kind of thing happens because every non-zero number has two square roots and the one we mean when we write #sqrt(...)# can be a slightly arbitrary choice.

So long as you stick to #a, b >= 0# then the rule holds:

#sqrt(ab) = sqrt(a)sqrt(b)#

When you get to deal with complex numbers more fully (in precalculus?) then it may become clearer.