Every positive number "n" has two square roots. One of them is positive ( 
or 
) , and the other is negative ( 
). Together, these are denoted as 
.
The principal square root is the positive number square root.
Unless otherwise stated, "the square root" of a number refers ONLY to the principal square root.
The square root of n2 is the absolute value of n.
This is a compact, consise way of expressing the following, (using the number 25 as an example):
When solving a simple equation such as x2 = 25, it must be observed that there are two solutions. The two solutions to this equation are 5 and -5, since both 52 = 25 and (-5)2 = 25.
The solution above shows all of the steps.
When someone is proficient with square roots, usually only the steps shown below are written out.
When working with equations involving the Pythagorean Theorem, it is important to remember that the lengths of the sides of the triangle are positive numbers.
