5.5 Roots of Real 5.5 Roots of Real NumbersNumbers

n bindex

radicand

radical sign

Note: square root when index is not visible

Square RootSquare Root

valuevalue squaresquare square square 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

The nThe nthth root root

if , then n na b b a

valuevalue nnthth power power nnthth root root

33 (3)(3)33 = 27 = 27

-2-2 (-2)(-2)55 = -32 = -32

3 27 3

5 32 2

Principal RootPrincipal Root

valuevalue nnthth root root principal principal 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

The nThe nthth root root if , then n na 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 25

1- root

32 2

n

1real root

0 0

ensures a nonnegative resultensures a nonnegative result

2 1( 5) ( 5) 5

** : ( ) ( )nNote even power odd power

6 3( 2) ( 2) 8 8