A real number r is called an nth root of b if rn = b.
In the following we assume b is a positive number, and n a positive integer.
(or ) is defined to be the positive nth root of b. Thus .
If n is even:
24 = 16 and (-2)4 = 16, so 161/4 = 2 and 161/4 = −2.
If n is odd:
105 = 100000, so 1000001/5 = 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 nth root.
In the following exercise, if the nth 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".