# SECTION 6.1 Definition of an nth Root

```SECTION 6.1
I.
Definition of an nth Root
OBJECTIVES
At the conclusion of this lesson you should be able to:
1.
2.
II.
Evaluate square roots.
PROCEDURE
While watching the video, follow this study guide and take notes in the study
guide as if you were sitting in a classroom. Stop or pause the video as needed to
catch up or copy something down.
n
a
a
Square root of a
3
a
4
a
5
a
n
a
195
Perfect Squares
12 = 1
6 2 = _____
112 = _____
16 2 = _____
22 = 4
7 2 = _____
12 2 = _____
17 2 = _____
3 2 = _____
8 2 = _____
13 2 = _____
18 2 = _____
4 2 = _____
9 2 = _____
14 2 = _____
19 2 = _____
5 2 = _____
10 2 = _____
15 2 = _____
20 2 = _____
Perfect Cubes
13 = 1
6 3 = ______
23 = 8
7 3 = ______
33 = ______
8 3 = ______
4 3 = ______
9 3 = ______
5 3 = ______
10 3 = ______
Perfect 4th’s
14 = 1
2 4 = 16
3 4 = ______
4 4 = ______
5 4 = ______
Perfect 5th’s
15 = 1
2 5 = 32
35 = ______
4 5 = ______
196
16 =
− 49 =
3
256 =
− 27 =
even
negative = NOT A REAL NUMBER
odd
negative = negative
− 81 =
25
=
49
3
8=
3
−8 =
4
197
− 16 =
Evaluating
n
a
Page 499
1.
If
n &gt; 1 is an even integer and a &gt; 0 , then
2.
If
n &gt; 1 is an odd integer, then
3.
If
n &gt; 1 is an integer,
n
n
a
1.
an
is the principal positive nth root of a.
0 =0 .
Example for #2
16 = _____
n
a
is the nth root of a.
Example for #1
Evaluating
n
3
27 = _____
3
− 27 = _____
Page 500
_________________________________________________________
n
______________________________________________
2.
an = a .
_________________________________________________________
n
______________________________________________
an = a .
Example for #1
Example for #2
3
23 = _______
4
2 4 = _______
3
(− 2)3
4
(− 2)4
= _______
198
= _______
Turn in your textbook to page 505.
Problem #52.
(− 5)2
Problem #56.
5
= _____
Problem #54.
6
(50)6
6
= _______
a 8b 4 c12
64x8
49a 6b8c10
3
= _______
Problem #58.
x2 y4
4
(− 2)5
− 27 a 6b 9
199
(− 417)6
= _______
32
x10
5
−
4
16 x8 y16
a 4b 2
c6
(x − 3)2
6
64a12
200
```