Radicals
For positive integer n and real number a, any real number x such that xn = a is called an nth root of a.
- For n = 2, an nth root is called a square root
- For n = 3, an nth root is called a cube root
- The principal nth root of a, which is the positive nth root of a is denoted by
![](/image/282/radical.gif)
- The principal nth root of 0 equals zero:
![](/image/289/radical_zero.gif)
- If a < 0, the principal nth root of a, is defined as a real number only when n is odd
Terminology:
The symbol
![](/image/287/radical_only.gif)
Considering:
![](/image/286/radical_examp.gif)
Properties of Radicals:
![](/image/288/radical_props.gif)
![](/image/286/radical_examp.gif)
It follows that:
index = 3,
radicand = 125,
principal 3rd root of radicand = 5
radicand = 125,
principal 3rd root of radicand = 5
Properties of Radicals:
![](/image/288/radical_props.gif)