Sec 1.2 –Revisiting Quadratics (Review) Simplifying Radicals Name:

PRODUCT RULE: QUOTIENT RULE:

√푥 ∙ 푦 = 푥푦 √

√ =

Example: Example:

√10 ∙ √푥 = √10푥 √ √

= = √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. √7푥 ∙ 2푦 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. 450푥 푦 7. √48푎 푏

M. Winking Unit 1-2 page 3

Express each radical in simplified form.

8. √80푎 푏 9. − 675푚 푛 푝 10.√−27푥

11.√6푥 ∙ √12푥 12.√12푎 푏 ∙ √6푎푏

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. 4 2 25 18 3 8 2x x x x 18. 3√24푥 + 2푥√3푥

M. Winking Unit 1-2 page 4

Simplify. Assume that all variable represent positive real numbers. 19. 2√6 3√2 − 5√3 20. 3√2 √6 + √12 − 2√3

21. 2√2푥 √12푥 − 4√6푥 + 3√3푥 22.√12 4√2 − 3√9

23. Consider the following rectangles.

a. Determine the Perimeter of the Rectangle. a. Determine the Perimeter of the Rectangle.

b. Determine the Area of the Rectangle. b. Determine the Area of the Rectangle.

2√10 + √6

2√6

2푥 + 3√6푥

6푥

M. Winking Unit 1-2 page 5

Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.

24. √

25. √

26. √√

27. √

28. 29. 2

2723812

30. √ √ √

√ 31. √

√ 32. √

√

M. Winking Unit 1-2 page 6