Problema Solution
What is the index of a radical? When working with radicals can the radicand be negative when the index is odd? Can it be negative when the index is even?
Please provide a problem that contains simplifying radicals.
Answer provided by our tutors
(a) Consider sqrt x. This is "second root" of x. Here 2 is called the index of the radical.
Similarly, for cube root x, which is the "thiird root" of x, 3 is the index of the radical.
In general, for the radical nth root x, n is called the index of the radical.
(b) Yes, it can be. For example, cube root of -8 is valid and the answer is -2
(c) No, it can't be. For example, sqrt -4 is not real. It is a complex number. Similarly,
fourth root -16 is not real.
(d) An example is: Simplify 3√-27 (Here 3 is a superscript - meaning cube root)