Square Roots
To square a number, we raise the number to the second power.
For example, 6^{2} = 36.
To find the square root of a number, we reverse the squaring process.
For example,
â€¢ one square root of 36 is 6, because 6^{2} = 36;
â€¢ another square root of 36 is 6, because (6)^{2} = 36.
Each positive real number has a positive square root and a negative
square root.
The positive square root is called the principal square root.
The radical symbol,
, is used to denote the principal square root
of a number.
For example, the principal square root of 36 is written like this:
Since the principle square root is the positive square root, we have:
The expression under the radical symbol is called the radicand.
Here, the radicand is 36:
A radical is the part of an expression that consists of a radical symbol and
a radicand.
A radical expression is an expression
that contains a radical.
In this example, the radical is


A negative number, for example 36, does not have square roots that are
real numbers. Thatâ€™s because a real number times itself always gives a
nonnegative number.
6^{2} = 36 
(6)^{2} = +36 
Definition â€”
Square Root
For a nonnegative real number, a, the principal square root of a is
written
.
If b is a nonnegative real number and b^{2} = a, then
Example:
because b is nonnegative and 6^{2}
= 36.
When you square the square root of a nonnegative number, the result is the
original number.
For example,
Likewise, when you take the square root of a nonnegative number squared,
the result is the original number.
For example,
