Index

Definition

The index of a radical is the small number written just outside and above the radical symbol. It indicates the degree of the root being taken.

5 Must Know Facts For Your Next Test

1. The index of a square root is 2, although it is usually not written.
2. For cube roots, the index is 3, and it must be written.
3. Changing the index changes the value of the radical expression.
4. When the index is even, only non-negative results are considered in real numbers.
5. The properties of exponents apply to radicals when rewriting them as rational exponents.

Review Questions

• What is the index in the radical expression $\sqrt[5]{32}$?
• How does changing the index affect a radical expression?
• What is implied about an index if it isn't written?

Related terms

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

Rational Exponents: $a^{m/n}$ represents taking the nth root of 'a' raised to the mth power.

Square Root: $\sqrt{x}$, which is equivalent to $x^{1/2}$, is a number that produces x when multiplied by itself.