What is the square root of 64?

3 Answers
Nov 21, 2016

#sqrt64=+-8#

Nov 21, 2016

Answer:

It's 8 or -8.

Explanation:

8 x 8 = 64.

Nov 21, 2016

Answer:

The principal square root of #64# is:

#sqrt(64) = 8#

The other (non-principal) square root is:

#-sqrt(64) = -8#

Explanation:

#64# has two square roots, namely #8# and #-8#, since:

#8^2 = (-8)^2 = 64#

When we say "the square root", what is usually intended is "the principal square root", which in the case of the Real square root of a positive number is the positive one.

Any non-zero number #n# has two square roots. In order to distinguish between them, we call one the "principal" square root, which in the case of #n > 0# means the positive one.

#color(white)()#
Complex footnote

If #n < 0# then it has two Complex non-Real square roots:

#+-i sqrt(-n)#

In this case we call #i sqrt(-n)# the principal square root and #-i sqrt(-n)# the non-principal one.

For example:

#sqrt(-64) = 8i# is the principal square root.

#-sqrt(-64) = -8i# is the other square root.

Note that #8i# is not "positive". Unlike Real numbers, Complex numbers are not ordered, but for pure imaginary square roots we choose the one with the positive imaginary part and call it "principal".