+

7.2 The Real nth Roots of a Number

+

1. How many values in the domain of f are paired with the value in the range? That is, how many x values satisfy the equation ?

f x

f x 9

x2 9

+

2. How many values in the domain of g are paired with the value in the range? That is, how many solutions are there of the equation ?

g x

g x 8

x3 8

+

3. How many values in the domain of h are paired with the value in the range? That is, how many solutions are there of the equation ?

h x

h x 2

x4 2

+

Definition:

Each solution of the equation , for n a positive integer, is called an

. Thus, 3 and -3 are the 2nd roots (or square roots) of 9, and -2 is the 3rd (or cube) root of -8.

xn b

nth root of b

+

+Solve over the real numbers.

4. 5. 1.21x2 1 27x3 125 0

+

The symbol is called a ; b is called the and n the . We say this as the nth root of b.

if n is odd

if n is even

bn radicalradicand index

bnn b

bnn b

+Find all real values for which the statement is true.

6. 7.

x 3 2

x 3

y 1 4 y 1 2