How do you simplify: the square root of -32?

1 Answer
Jul 25, 2015

Answer:

The square roots of #-32# are #+-4sqrt(2) i#

Explanation:

The identity #sqrt(ab) = sqrt(a)sqrt(b)# is only valid for #a, b >= 0#.

About the best we can do more generally is #sqrt(ab) = +-sqrt(a)sqrt(b)#

To see why, consider the invalid reasoning:

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

With this in mind:

#sqrt(-32) = sqrt(4^2*2*-1) = +-sqrt(4^2)sqrt(2)sqrt(-1) = +-4sqrt(2)i#