Math 101 Intermediate Algebra
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Roots and Radical
Chapter 8, Section 1


Roots and Radicals
A radical expression is .

  is the radical sign, a is the radicand, and m is the index.

  means the square root of a.

The principal (or positive) square root of the number a is written   and is equal to the positive number whose square equals a.

For this class, "square root" means principal square root.

  means the cube root of a.

  means the mth root of a.

    if  bm = a.


Even Indexes

The mth root of a,   ,  where m is an even index and a is a positive real number, is that positive real number b such that  bm = a.

Example:    =  3 since 34 = 81.


Odd Indexes

The mth root of a,   ,  where m is an odd index and a is any real number, is that real number b such that  bm = a.

Example:    =  4 since 43 = 64.

Example:    =  -4 since (-4)3 = -64.


Square Roots of Something Squared

Consider any real number squared. It's square root is the absolute value of that real number.

Example:    =  |a|

Example:    =  |-6|  =  6

Example:    =  |x - 2|