Odd and Even kth Roots

Odd and Even kth Roots

In the expression , we call k the index and assume k ≥2.

ODD ROOTS

The 5th root of a number a is the number c for which  c⁵ = a. There are also

7th roots, 9th roots, and so on. Whenever the number k in is an odd

number, we say that we are taking an odd root.

 

Every number has just one real-number odd root. For example, = 2, = -2  and  = 0.If the number is positive, then the root is positive.

If the number is negative, then the root is negative. If the number is 0, then the

root is 0. Absolute-value signs are not needed when we are finding odd roots.

If k is an odd natural number, then for any real number a,

= a.