Section 1-8 Radical Rules
PRODUCT RULE:
QUOTIENT RULE:
√ ∙
√ =
√ =
Example:
Example:
√10 ∙ √ = √10
√
√ =
= √5
More directly, when determining a product or quotient of radicals and the indices (the small number in front
of the radical) are the same then you can rewrite 2 radicals as 1 or 1 radical as 2.
Simplify by rewriting the following using only one radical sign (i.e. rewriting 2 radicals as 1).
1. √3 ∙ √12
3.
√7 ∙ 2
2. 4.
√
√
√
√
Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2).
5.
6.
M. Winking (Section 1-8)
p. 17
Express each radical in simplified form.
7. √48
8.
450
9.
P
10. √300
N
11.
675
48
O
12. − 81
O
13.
72
N
81
14.
A
15. √−27
N
I
K
Use the letters and answers to match the answer to the riddle. Only some answers will be used.
“What is an opinion without π?”
_________
−9
√
_________
15
2
_________
10
√3
_________
_________
_________
2
3
6
√6
√3
√2
_________
15
M. Winking (Section 1-8)
3
p. 18
Express each radical in simplified form.
16.√6 ∙ √12
17.√18
∙ √6
Simplify. Assume that all variable represent positive real numbers.
18. 5√3 + √2 − 2√3 + 4√2
21.
√18 − 3 12

19.
+2 8
24. 2 10 3 6  2 5  24
√32
22.

108  5 12  4 44
25.
2x
23. 5 18 x 4  3x 8 x 2  x 2 2
+ 2 √18

6x  3 x
20. 2 150  18  3 8  24

26. 3 6a

4a  2 15a 2

p. 101
M. Winking (Section 1-8)
p. 19
Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.
18.
21.
√
19.
20.
√
22.
12  8 3  2 27
2
√
√
23.
√
√
√
√
M. Winking (Section 1-8)
p. 20