In
m is the index or order
Ö is the radical or square root sign
a is the radicand
Radicals involve the use of the radical sign (√). Sometimes these are also called surds.
 Square root:
A number that must be multiplied times itself to equal a given number. The square root of a is written √a or a^{1/2}.
 Cube root:
A number that must be multiplied times itself three times to equal a given number. The cube root of a is written or ^{3}√a or a^{1/3}.
 4th root, 5th root or nth root:
The number that must be multiplied times itself m times to equal a given value. The m^{th} root of a is written ^{m}√a or a^{1/m}.
Example, ^{5}√32 = 2 since 2^{5} = 32.
Note: When m = 2 an m^{th} root is called a square root.
When m = 3 an m^{th} root is called a cube root.
When m = 4 an m^{th} root is called fourth root.
When m = 5 an m^{th} root is called fifth root.
and so on......
If m is even and a is negative, then ^{n}√x is non real.
A surd or a radical is an expression containing a root with an irrational solution that can not be expressed exactly.
For example: √3 = 1.732050808......
For any real number a and any integer m, m>1, the principal nth root of a can be described as follows:
If a > 0 then is a positive real number.
If a = 0, then is zero.
If a < 0, and n is odd, then is a negative real number.
If a < 0, and n is even, then is not a real number.
Example:
^{5}Ö3
3 is a positive rational number
^{5}Ö3 is a surd with 5^{th} order.
Directions: Choose the correct answer. Also write at least 10 examples of your own for square root, cube root and nth root.
