22 Jun The principal square root of ##64## is: ##sqrt(64) = 8## The
The principal square root of ##64## is: ##sqrt(64) = 8## The other (non-principal) square root is: ##-sqrt(64) = -8## ##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.
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