The Root of Odd Degree n From Negative number a

Suppose `a<0` and `n` is natural number and is greatest than 1.

If `n` is even number, then equality `x^n=a` doesn′t execute for any real number `x`.

This means, that in the range of real numbers is impossible to determine the root of an even degree from a negative number.

If `n` is odd number, then there is only one real number `x`, that `x^n=a`. This number is denoted as `root(n)(a)` and called the root of odd degree `n` from negative number `a`.

For example, `root(3)(-8)=-2`, as `(-2)^3=-8` ; `root(5)(-243)=-3` , as `(-3)^5=-243`.

The properties of radicals are equitable for nonnegative values of the radicand expression and correct for negative values of the radicand expression in the case of odd exponents of roots.

For example, `root(3)(ab)=root(3)(a)*root(3)(b)` for any `a` and `b`.