Question

Part 1: Explain, in complete sentences, how a higher order root is different from a square root. Part 2: Give two examples.

Answer 1

A higher order root describes:
\[\sqrt[n]{x} = x^{1/n}\] or "fractional exponents". As \[n \rightarrow \infty,~1/n \rightarrow 0\]. If 1/n approaches 0, then \[x^{1/n} \rightarrow 1\] since \[x^{0} = 1\]. Try to come up with some examples on your own, then check back.