Higher order roots, radicals, and nth roots are all related concepts in mathematics. Higher order roots can be also called higher index roots, nth roots or radicals.
Higher order roots, are like square roots, but instead of finding a number that can be multiplied by itself to get the original number, we find a number that can be multiplied by itself a certain number of times to get the original number.
For example:
The cube root of 27 is 3, because 3 x 3 x 3 = 27
The fourth root of 16 is 2, because 2 x 2 x 2 x 2 = 16
We usually write the cube root symbol like this: ∛, and the fourth root symbol like this: ⁴√. So, ∛27 means the cube root of 27, and ⁴√16 means the fourth root of 16.
A higher order root, or nth root, is simply a root with a larger index, such as a fifth root or a sixth root. For example, the fifth root of 32 is 2 because 2 x 2 x 2 x 2 x 2 = 32.
So, to put it simply, nth roots are a type of higher order roots that are represented using radicals, and they tell us what number, when multiplied by itself a certain number of times, gives the original number.
It's important to note that, like square roots, there can be multiple answers to higher index roots. For example, both -2 and 2 are fourth roots of 16.