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.
â€¢ one square root of 36 is 6, because 62 = 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
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 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
For a nonnegative real number, a, the principal square root of a is
If b is a nonnegative real number and b2 = a, then
because b is nonnegative and 62
When you square the square root of a nonnegative number, the result is the
Likewise, when you take the square root of a nonnegative number squared,
the result is the original number.