How do you simplify #sqrt(-9)#?

1 Answer
Feb 19, 2016

Answer:

#sqrt(-9) = 3i#

Explanation:

If #x < 0# then #sqrt(x) = sqrt(-x)i#, where #i# is the imaginary unit.

#i# has the property that #i^2 = -1#

In our example, we find:

#sqrt(-9) = sqrt(9)i = 3i#

Note that special care is required when dealing with square roots of negative numbers. In particular #sqrt(ab) != sqrt(a)sqrt(b)# if both #a < 0# and #b < 0#.

For example:

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