


Exponentsn^{th} RootA real number r is called an n^{th} root of b if r^{n} = b. The 2^{nd} root is also called the square root and the 3^{rd} root is called the cube root. In the following we assume b is a positive number, and n a positive integer. Notation: (or ) is defined to be the positive n^{th} root of b. Thus . . .
If n is even:
Example2^{4 }= 16 and (2)^{4} = 16, so 16^{1/4} = 2 and 16^{1/4} = −2. If n is odd:
Examples10^{5} = 100000, so 100000^{1/5} = 10. (10)^{5 }= −100000, so (−100000)^{1/5} = 10. Have a look at a few more examples. Any decimal roots are approximate only. None means the number does not have an n^{th} root.
ExerciseIn the following exercise, if the n^{th} root exists and is an integer display it in the box provided. If it exists but is not an integer, type NI for "not integer". Otherwise, if the root does not exist, type N for "no solution". << Cube Root  Exponents Index  General Fractional Exponents >>
