1.4    Vocabulary for Radical Equations and Functions                            

Cube Root:  a number or expression taken as a factor three times to obtain a perfect cube.  

Equivalent Equations:  Equations that have the same solution.

The equations  are equivalent because the solution for each  equation is the same, x = 2.

Other pairs of Equivalent equations:              

Pairs that are NOT equivalent:              

Extraneous Solution       An EXTRA solution that is found when the equation is solved

correctly, but when put back into the original equation causes the equation to be undefined or false.  Frequently the act of squaring both sides (or taking both sides to any even power) results in an extraneous solution.

Index

The number indicating the root to be taken.

Perfect Square:  A number, variable or quantity that is the result of something being squared, or multiplied by itself

Perfect Cube:   A number, variable or quantity that is the result of something being cubed, or multiplied by itself three times

Quadratic equation:  An equation of degree two:

             Quadratic equations:                         

             Equations that are NOT quadratic:    

Radical:   The root of a quantity as indicated by the radical sign.  See square root and cube root.   The word comes from the Latin rdix, meaning root.

Radical sign:   The sign  indicating extraction of roots.  The index designates the root to be taken.

                This radical has an index of 3:          

                indicating that we want the cube, or third, root:   

Radicand:  The number or expression under the radical sign.

                           The expression    has a radicand of 5;

                           The expression    has a radicand of ;

                         The expression    has a radicand of ;

Rational number

A number that can be written in the form , where a and b are integers and . As a decimal, rational numbers either terminate (end) or repeat.  Click here to review all subsets of real numbers.

Square Root:  a number or expression taken as a factor two times to obtain a perfect square. 

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