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 Sec 1.2 –Revisiting Quadratics
(Review) Simplifying Radicals
Name: PRODUCTRULE: QUOTIENTRULE:
√ ∙
√ √ Example:
√10 √
Example: √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. √7 ∙ 2 2. √
√
Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2). 3. 4. Express each radical in simplified form. 5. √48 6. 450
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7. √48
Express each radical in simplified form. 8. √80
9. 675
10.√ 27
∙ √6
11.√6 ∙ √12 12.√12
Simplify. Assume that all variable represent positive real numbers. 13. 5√3 √2 2√3 4√2 14. 108
 5 12  4 44 15. 2 12 
18  2 3  3 8 16. √16 √108 2√54 17. 5 18 x
4
 3x 8x 2  x 2 2 18. 3√24
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2 √3 Simplify. Assume that all variable represent positive real numbers. 19. 2√6 3√2 5√3 √12
20. 3√2 √6
3√3
22.√12 4√2 2√3 21. 2√2 √12
4√6
3√9 23. Consider the following rectangles. 2√6 6
2√10 √6 a. Determine the Perimeter of the Rectangle. b. Determine the Area of the Rectangle. 2
3√6 a. Determine the Perimeter of the Rectangle. b. Determine the Area of the Rectangle. M.WinkingUnit1‐2page5
Simplify. Assume that all variable represent positive real numbers and rationalize all denominators. 24. √
√
√
25. 26. 28. 29. 31. 32. √
27. √
12  8 3  2 27
2
√
30. √
√
√
√
√
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√
√