Principal Value of a Square Root

A square root of a number b is the solution of the equation x 2 =b .  It is a number that when multiplied by itself gives you b .  Every positive number b has two square roots, denoted b and b .  The principal square root of b is the positive square root, denoted b .

Example 1:

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

The principal square root of 25 is 25 =5

Example 2:

Find the real roots of the equation x 2 =100 .

x=± 100 =±10

Therefore the roots are 10 and 10 .

Example 3:

Simplify 36

36  indicates the principal (or positive) square root so 36 =6