Simplifying and Combining Radical Expressions

Learn about simplifying radical expressions, rewriting them in different forms, identifying like radicals for addition and subtraction, and using quotient rule to divide radicals. Explore examples and hints to practice the concepts effectively.

• Radical Expressions
• Simplification
• Like Radicals
• Quotient Rule
• Division

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1. Check Simplify 25 81?4 1) 2)

2. Check 1 7 6 4 7 3) 6 4) 49 1 Rewrite in radical notation 2 5 2 5) ?? Rewrite with radical exponents 513? 6)

3. Check Simplify 7) 7 5 8) 28 9) 381?8?6 39?4?12 10) 36?7?

5. Chapter 7 Section 4 Adding, Subtracting, and Dividing Radical Expression Page 533

6. Adding and Subtracting Radical Expressions The process is the same for combining similar terms. 7 2+4 2 7+4 ( 11 2 7x + 5x (7 + 5) x 12 x ) 2

7. Like Radicals Two or more radical expressions that have the same indices and the same radicands. Which are like radicals? a b Like radicals can be added, subtracted. Leave the radical and add 3 7 11,? 6 5,? 6 11 ,? 2 5 c d 7 11+6 11

8. Try 7 3+2 3 8 17-5 19-6 17+4 19 Hint: Write the like radicals together before doing the operation.

9. Simplify Before Combining Radicals 8 18-5 8 a) 4 27x +8 12x b)

10. Higher Indices - Simplify -4? 54 3 3 2? 16 a) +? 27x5y4 5? x2y 3 3 b)

11. Dividing Radical Expression Observe 64 4 64 4 64 4 16 4 8 2 4

12. The Quotient Rule for Radicals Page 536

13. Using the Quotient Rule to Simplify Radicals Simplify 16 27 3 a) x2 b) 25y6

14. Dividing Radical Expressions Dividing radicals, write the radicand as a single fraction then simplify Example 16x5y2 2x 3 48x3 6x 3 16x5y2 2x 48x3 6x 3

15. Try 200x3 10x-1 a) 72xy 2 2 b)

16. Summary Add, subtract like radicals Leave index and add, subtract coefficients. Divide like radicals Write as a single radical and simplify