# Key Concepts & Glossary

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

*n*th root*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

## Licenses & Attributions

### CC licensed content, Specific attribution

- College Algebra.
**Provided by:**OpenStax**Authored by:**OpenStax College Algebra.**Located at:**https://cnx.org/contents/[email protected]:1/Preface.**License:**CC BY: Attribution.