- Roots and Radicals
- A radical expression is
 .
-
 is the radical sign,
a is the radicand, and
m is the index.
-
 means the square root of a.
- The principal (or positive) square root of the number a is written and is equal to the positive number whose square equals a.
- For this class, "square root" means principal square root.
-
 means the cube root of a.
- means the mth root of a.
-
 if bm = a.
- Even Indexes
- The mth root of a,
,
where m is an even index and a is a
positive real number, is that positive
real number b such that bm = a.
- Example:
 = 3 since 34 = 81.
- Odd Indexes
- The mth root of a,
,
where m is an odd index and a is
any
real number, is that real number b such that bm = a.
- Example:
 = 4 since 43 = 64.
- Example:
 = -4 since (-4)3 = -64.
- Square Roots of Something Squared
- Consider any real number squared. It's square root is the absolute value of that real number.
- Example:
 = |a|
- Example:
 = |-6| = 6
- Example:
 = |x - 2|
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