SIMPLIFYING RADICAL EXPRESSIONS
1, 4, 9, 16, 25, ____, ____, ____, ____, ____, ____, 144…
Perfect Squares:
x2, x4, x6, ____, ____... Exponents must be __________.
25 is read “the square root of 25”.
25 = 5 because 52 = 25
36 = 6 because ____ = ____
100 = _____
49 = _____
a 6 = a 3 because (a3)2 = a6
m16 = m8 because ____ = ____
y10 = _____
a 2 = _____
Hint: Divide the exponent by _______.
In the expression
a , the
is called the radical and a is called the radicand.
Simplify (Simplifying Perfect Squares):
1.
4
2.
16
3.
100
4.
a8
5.
6.
a 6 b10
7.
9a 2
8.
81m 64
9.
49a 4b12
10.
w12
121x14 y 6
Simplify (Simplifying Radicals that are not Perfect Squares):
1.
20 = 4 • 5 = 2 5
4.
7.
a5 = a 4 a = a 2 a
2.
3.
5.
6.
8.
9.
48 = 16 3 = 4 3
=
Simplify:
1.
18
2.
125
3.
72
4.
180
6.
b7
7.
m11
8.
75 x 7 y 5
9.
27a11b 7
11.
9a 8
12.
45a 7
13.
16.
196
17.
63x 4 y
18.
36 x 2 y 6
14.
19.
12 x 20 y 8
5.
10.
15.
20.
a3
32a 7 b 4
200
Homework Simplifying Radicals
Name __________________
Class Time________
Simplify each of the following expressions completely.
________ 1.
64
________ 2.
18
________ 3.
32
________ 4.
50
________ 5.
400
________ 6.
x6
________ 7.
x7
________8.
16x16
________9.
9x 9
________10.
40x 8
________11.
25x 7
________12.
12x 5
________13.
a 2b 4
________14.
49a 8 x12
________15.
28 x 9 y 6
________16.
32m 7 n11
________17.
20 x10 y 5
________18.
100ab 4
________19.
75 x 8 y 3
________20.
98 x 7 y 5
________21.
Homework: This worksheet
Answers to odd problems on worksheet:
1. 8
3. 4 2
13. ab2
15. 2 x 4 y 3 7 x
5. 20
7. x 3 x
17. 2 x 5 y 2 5 y
9. 3x 4 x
19. 5 x 4 y 3 y
11. 5 x 3 x
21.