Easy Algebra Step-by-Step

36 Easy Algebra Step-by-Step

f. − 22 ⋅−

Step 1. Find the principal square root of − 22 ⋅−.

− 22 ⋅− =− 22 =

g. bb

Step 1. Find the principal square root of bb.

bbb=b

Cube Roots and nth Roots

A number x such that xxxxx =c is a cube root of c. Finding the cube root of

a number is the reverse of cubing a number. Every real number has exactly

one real cube root, called its principal cube root. For example, because

− 444 ⋅−⋅− =− 64 , − 4 is the principal cube root of − 64. You use^3 − 64 to

indicate the principal cube root of − 64. Thus,^3 −= 64 − 4. Similarly,^364 = 4.

As you can see, the principal cube root of a negative number is negative, and

the principal cube root of a positive number is positive. In general, if x is

a real number such that xxxxx =c, then^3 cx. Here is a list of principal

cube roots of some perfect cubes that are useful to know.

(^300) , (^311) ,^382 ,^327 = 3 ,
(^364) = 4 , (^3125) = 5 , (^31000) = 10
If a number is not a perfect cube, you indicate its principal cube root by
using the cube root symbol. For instance, the cube root of − 18 is^3 − 18.
Problem Find the indicated root.
a.^3 − 27
b.
8
125
3
c.^3 0 008.
d.^3 − 1
You will fi nd it worth your while to
memorize the list of cube roots.
− 22 ⋅−≠− − 2. The symbol
never gives a negative number as
an answer.
bb⋅≠b b if b is negative and bb≠ if
b is negative. Because you don’t know
the value of the number b, you must
keep the absolute value bars.