nth Root
The nth root of a number x, where n is a positive integer, is a number r whose nth power is x:
Every positive real number x has a single positive nth root, which is written . For n equal to 2 this is called the square root and the n is omitted. The nth root can also be represented using exponentiation as x1/n.
For even values of n, positive numbers also have a negative nth root, while negative numbers do not have a real nth root. For odd values of n, every negative number x has a real negative nth root. For example, −2 has a real 5th root, but −2 does not have any real 6th roots.
Every non-zero number x, real or complex, has n different complex number nth roots including any positive or negative roots, see complex roots below. The nth root of 0 is 0.
For most numbers, an nth root is irrational. For example,
All nth roots of integers, or in fact of any algebraic number, are algebraic.
For the extension of powers and roots to indices that are not positive integers, see exponentiation.
The character codes for the radical symbols are
| Read | Character | Unicode | ASCII | URL | HTML |
|---|---|---|---|---|---|
| Square root | √ | U+221A | √ |
%E2%88%9A |
√ |
| Cube root | ∛ | U+221B | ∛ |
%E2%88%9B |
|
| Fourth root | ∜ | U+221C | ∜ |
%E2%88%9C |
Read more about nth Root: Identities and Properties, Simplified Form of A Radical Expression, Infinite Series, Computing Principal Roots, Solving Polynomials
Famous quotes containing the word root:
“...there is hope for a tree, if it is cut down, that it will sprout again, and that its shoots will not cease. Though its root grows old in the earth, and its stump dies in the ground, yet at the scent of water it will bud and put forth branches like a young plant. But mortals die, and are laid low; humans expire, and where are they?”
—Bible: Hebrew, Job 14:7-10.