Easy Algebra Step-by-Step

Roots and Radicals 39

(^6) −≠ 11 ≠−. (^) − 111111 ⋅−⋅−⋅−⋅−⋅−= 1 ,
not − 1.
c.^30.^125
Step 1. Find the principal cube root of 0.125.
()^05.^5 ()^0505 ... ()^005. =^0.^125 , so^30 ..^125125 =^005.
d.^6 − 1
Step 1. − 1 is negative and 6 is even, so^6 − 1 is
not a real number.
(^6) − 1 is not defi ned for real numbers.
e.^7 − 1
Step 1. Find the principal seventh root of − 1.
−= 1111111 ⋅− ⋅−⋅−⋅− ⋅−⋅− − 1 , so^7 − 11 =−.
f.^500
Step 1. Find the principal 50th root of 0.
The nth root of 0 is 0, so^5000.

Simplifying Radicals

Sometimes in algebra you have to simplify radicals—most frequently,

square root radicals. A square root radical is in simplest form when it has

(a) no factors that are perfect squares and (b) no fractions. You use the

following property of square root radicals to accomplish the simplifying.

If a and b are nonnegative numbers,

abb= ab

Problem Simplify.

a. 48

b. 360

P