The principal square root is the non-negative square root.
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The principal square root of 9, the positive integer which is the square root of the number, is 3.
The principal (positive) square root of 225 is 15.
If unspecified, the square root is the principal root, which is the positive root.
The principal square root is a positive number which, when multiplied by itself, gives the original number. The second square root is the negative of the principal square root. So, for example, starting with 144. The principal square root is 12 because 12*12 = 144 and the second square root is -12.
A positive number has two square roots, that is, there are two solutions to an equation like x2 = 100. The "principal square root" refers to the positive solution.