Square Roots
To square a number, we raise the number to the second power.
For example, 62 = 36.
To find the square root of a number, we reverse the squaring process.
For example,
• one square root of 36 is 6, because 62 = 36;
• 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. That’s because a real number times itself always gives a
nonnegative number.
Definition —
Square Root
For a nonnegative real number, a, the principal square root of a is
written
.
If b is a nonnegative real number and b2 = a, then
Example:
because b is nonnegative and 62
= 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,
