The document discusses roots of real numbers, including how to calculate square roots, nth roots, and principal roots. It explains that the nth root of a number a is the value b such that bn = a, and that the principal root ensures a nonnegative result. When there is more than one real root, the principal root is the nonnegative root.

1. 5.5 Roots of Real5.5 Roots of Real
NumbersNumbers

2. n
b
index
radicand
radical sign
Note: square root when index is not visible

3. Square RootSquare Root
valuevalue squaresquare squaresquare
rootroot
55 (5)(5)22
= 25= 25
-3-3 (-3)(-3)22
= 9= 9
25 5=
9 3= −
 The inverse of squaring a valueThe inverse of squaring a value

4. The nThe nthth
rootroot
if , thenn n
a b b a= =
valuevalue nnthth
powerpower nnthth
rootroot
33 (3)(3)33
= 27= 27
-2-2 (-2)(-2)55
= -32= -32
3
27 3=
5
32 2− = −

5. Principal RootPrincipal Root
valuevalue nnthth
rootroot principalprincipal
rootroot
6
3−
 When there is more than 1 real root,When there is more than 1 real root,
the nonnegative rootthe nonnegative root
36
3
27− 3−
6±

6. The nThe nthth
rootroot
if , thenn n
a b b a= =
nn
eveneven --------------------
oddodd --------------------
eithereither ------------------ --------------------
1+ and 1- root
49 7= ±
b is neg.(-)b is pos.(+) b is 0
no real root
25−
3
1 + root
8 2=
5
1- root
32 2− = −
n
1real root
0 0=

7.  ensures a nonnegative resultensures a nonnegative result
2 1
( 5) ( 5) 5− = − =
** : ( ) ( )nNote even power odd power=
6 3
( 2) ( 2) 8 8− = − = − =