What is the negative square root of 27?

1 Answer
George C.
Jul 14, 2015

The negative square root of #27# is #-sqrt(27) = -3sqrt(3)#

Explanation:

#x^2=27# has two solutions, which we call #+-sqrt(27)#

#sqrt(27)# denotes the positive square root.

#-sqrt(27)# is also a square root of #27#, which we call the negative square root of #27#

If #a, b >= 0# then #sqrt(ab) = sqrt(a)sqrt(b)#.

So:

#-sqrt(27) = -sqrt(3^2*3)=-sqrt(3^2)sqrt(3) = -3sqrt(3)#

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