Sec 1.2 –Revisiting Quadratics
(Review) Simplifying Radicals
PRODUCT RULE:
𝑎
𝑎
Name:
QUOTIENT RULE:
𝑎
√𝑥
√𝑦
𝑎
𝑥
𝑎
√𝑥 ∙ √𝑦 = √𝑥𝑦
𝑎
= √
𝑦
Example:
Example:
√10 ∙ √𝑥 = √10𝑥
√10
√2
=√
10
2
= √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
√7𝑥 ∙ √2𝑦
2.
√12𝑥 2
3
√4𝑥
Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2).
𝑥6
144
4. √121
3. √ 25
Express each radical in simplified form.
5. √48
6.
√450𝑥 4 𝑦 5
M. Winking
7.
Unit 1-2 page 3
3
√48𝑎7 𝑏 3
Express each radical in simplified form.
4
8. √80𝑎10 𝑏3
9.
−√675𝑚4 𝑛11 𝑝5
3
10. √−27𝑥 5
12. √12𝑎3 𝑏 5 ∙ √6𝑎𝑏 2
11. √6𝑥 ∙ √12𝑥
Simplify. Assume that all variable represent positive real numbers.
13. 5√3 + √2 − 2√3 + 4√2
3
3
3
16. √16 − √108 + 2 √54
14.
108  5 12  4 44
17. 5 18 x
4
 3x 8 x 2  x 2 2
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Unit 1-2 page 4
15. 2 12 
3
18  2 3  3 8
3
18. 3√24𝑥 4 + 2𝑥 √3𝑥
Simplify. Assume that all variable represent positive real numbers.
19. 2√6 (3√2 − 5√3)
20. 3√2 (√6 + √12 − 2√3)
3
21. 2√2𝑥 (√12𝑥 − 4√6𝑥 3 + 3√3𝑥)
3
3
22. √12 (4 √2 − 3 √9)
23. Consider the following rectangles.
√6𝑥 3
2√6
2√10 + √6
a. Determine the Perimeter of the Rectangle.
√2𝑥 2 + 3√6𝑥
a. Determine the Perimeter of the Rectangle.
b. Determine the Area of the Rectangle.
b. Determine the Area of the Rectangle.
M. Winking
Unit 1-2 page 5
Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.
24.
27.
30.
3
25.
√5
12
2√6
6
√3
26.
16
27
28. √
√2(√12−√3)
√3
29.
3𝑥√2
√6𝑥
31. 2
32.
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Unit 1-2 page 6
3√2
√6
12  8 3  2 27
2
√6
√2𝑥 3