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)