Vocabulary - Radicals And Rational Exponents

Front 1

Power

Back 1

An expression written with a base and an exponent or the value of such an expression

4^2

Front 2

Base

Back 2

The number in a power that is used as a factor.

In 2^3,
2 is the base.

Front 3

Exponent

Back 3

The number that indicates how many times the base in a power is used as a factor

In 2^3,
3 is the exponent

Front 4

Radicand

Back 4

The expression under the radical sign

In ∛27,
27 is the radicand

Front 5

Index

Back 5

In the radical √(n&x), which represents the nth root of x, n is the index. In the radical √x, the index is understood to be 2.

In ∛27,
3 is the index

Front 6

Rational Exponent

Back 6

An exponent that can be expressed as m/n such that if m and n are integers, then b^(m/n)= √(n&b^m )=(〖√(n&b) )〗^m

In, 4^(3/2)
3/(2 ) is the rational exponent

Front 7

Radical function

Back 7

A function whose rule contains a variable within a radical

f(x) = ∛x

Front 8

Square root function

Back 8

A function whose rule contains a variable under a square root sign.

f(x)= √x

Front 9

Radical equation

Back 9

An equation that contains a variable within a radical

2√(x+1)=14

Front 10

radical inequality

Back 10

An inequality that contains a variable within a radical

√(x-3)+ 2≤5

Front 11

Extraneous solution

Back 11

A solution of a derived equation that is not a solution of the original equation

-2 is an extraneous solution to √(x+18)=x-2

Front 12

like radical terms

Back 12

Radical terms having the same radicand and index

∛27and 4∛27

Front 13

domain

Back 13

The set of all possible input values of a relation or function

Front 14

range

Back 14

The set of all possible output values of a relation or function

Front 15

simplify

Back 15

To perform all indicated operations

3∛8= 6