What is the square root of -3?

1 Answer
George C.
Sep 10, 2015

#-3# has no Real square root.

The principal Complex square root of #-3#, denoted #sqrt(-3)# is equal to #i sqrt(3)#, where #i# is the imaginary unit and #sqrt(3)# is the positive square root of #3#.

Explanation:

There is no Real number that is the square root of #-3# since #x^2 >= 0# for all #x in RR#.

#-3# has two Complex square roots, #i sqrt(3)# and #-i sqrt(3)#, where #i# is the imaginary unit, approximately called 'the' square root of #-1#. #i# satisfies #i^2 = -1#.

#sqrt(3)# is the positive square root of #3#.

#-sqrt(3)# is also a square root of #3#, in that #(-sqrt(3))^2 = 3#

#sqrt(-3) = i sqrt(3)# is called the principal square root of #-3#.

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