Can -5 be the square root of 25?

2 Answers
Sep 15, 2015

Answer:

Yes

Explanation:

#5 xx 5 =25#
Hence 5 is the square root of 25.

Sep 15, 2015

Answer:

#-5# is a square root of #25# in that #(-5)^2 = 25#

When we say the square root of a positive number, we usually mean the positive square root, also known as the principal square root.

Explanation:

Any non-zero number has exactly #2# square roots.

Actually in a technical sense #0# has #2# square roots, but they are both #0#.

If #x > 0# then #sqrt(x)# denotes the positive square root and #-sqrt(x)# denotes the negative one.

If #x < 0# then #sqrt(x) = i sqrt(-x)# denotes the square root with positive coefficient of #i# (the imaginary unit). #-sqrt(x) = -i sqrt(-x)# is the other square root.

If #z# is Complex, then it still has exactly two square roots, but different people use different conventions as to which one is the principal square root (i.e. the one represented as #sqrt(z)#).

In terms of polar representation, this boils down to choosing whether you prefer to use angles in the range #(-pi, pi]# or #[0, 2pi)# for #z#, resulting in angles in the range #(-pi/2, pi/2]# or #[0, pi)# for #sqrt(z)#.