Index

Definition

In the context of radicals, the index specifies the root being taken. For example, in $\sqrt[n]{x}$, 'n' is the index and indicates an n-th root.

5 Must Know Facts For Your Next Test

1. The default index for square roots is 2 and is often not written explicitly.
2. When the index is 3, it refers to a cube root.
3. The index must be a positive integer greater than or equal to 2.
4. Changing the index changes which root you are taking; for example, $\sqrt[4]{16}$ means finding the fourth root of 16.
5. In rational exponents, an expression like $x^{m/n}$ corresponds to $\sqrt[n]{x^m}$ where 'n' is the index.

Review Questions

• What is the default value of an omitted index in a radical?
• How does changing the index from 3 to 4 affect the radical expression?
• In $\sqrt[5]{32}$, what does '5' represent?

Related terms

Radical:

An expression that includes a root symbol ($\sqrt{}$) with an indicated radicand.

Rational Exponent:

An exponent that can be expressed as a fraction where $a^{m/n} = \sqrt[n]{a^m}$.

Radicand:

The number or expression inside a radical symbol that is subject to rooting.