Section 4-2
4 Radicals
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)
1.
√7 ∙ 2
2.
√
√
Simplify by rewriting the
he following using multiple radical sign (i.e. rewriting 1 radical as 2).
2)
3.
4.
Express each radical in simplified form.
5. √48
6.
450
7. √48
Express each radical in simplified form.
8. √−27
9. − 675
11.√6 ∙ √12
10. √80
12.
64 Simplify. Assume that all variable represent positive real numbers.
13. 5√3 + √2 − 2√3 + 4√2
16. √24
+ √3
14.
16. 2
4
32
− 3 162
2
15. 5 18 x  3 x 8 x  x
108  5 12  4 44
+ 2
17.
2x

6x  3 x

2
2
Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.
18.
√
21.
24.
19.
22.
√
√
25.
√
√
20.
√
12  8 3  2 27
2
√
√
23.
√
26.
√
√
√
√
√