Principal Value of a Square Root

A square root of a number b is the solution of the equation x2 = b.  It is a number that when multiplied by itself gives you b.  Every positive number b has two square roots, denoted and – .  The principal square root of b is the positive square root, denoted .

Example 1:

The square roots of 25 are and since 52 = 25 and (–5)2 = 25.

The principal square root of 25 is

Example 2:

Find the real roots of the equation x2 = 100.

Therefore the roots are 10 and –10.

Example 3:


 indicates the principal (or positive) square root so