## Key Concepts

- The principal square root of a number [latex]a[/latex] is the nonnegative number that when multiplied by itself equals [latex]a[/latex].
- If [latex]a[/latex] and [latex]b[/latex] are nonnegative, the square root of the product [latex]ab[/latex] is equal to the product of the square roots of [latex]a[/latex] and [latex]b[/latex]
- If [latex]a[/latex] and [latex]b[/latex] are nonnegative, the square root of the quotient [latex]\frac{a}{b}[/latex] is equal to the quotient of the square roots of [latex]a[/latex] and [latex]b[/latex]
- We can add and subtract radical expressions if they have the same radicand and the same index.
- Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.
- The principal
*n*th root of [latex]a[/latex] is the number with the same sign as [latex]a[/latex] that when raised to the*n*th power equals [latex]a[/latex]. These roots have the same properties as square roots. - Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals.
- The properties of exponents apply to rational exponents.

## Glossary

**index** the number above the radical sign indicating the *n*th root

**principal nth root** the number with the same sign as [latex]a[/latex] that when raised to the

*n*th power equals [latex]a[/latex]

**principal square root** the nonnegative square root of a number [latex]a[/latex] that, when multiplied by itself, equals [latex]a[/latex]

**radical** the symbol used to indicate a root

**radical expression** an expression containing a radical symbol

**radicand** the number under the radical symbol