NAME DATE PERIOD 10-3 Study Guide and Intervention

NAME

DATE

PERIOD

10-3 Study Guide and Intervention

Operations with Radical Expressions

Add or Subtract Radical Expressions When adding or subtracting radical

expressions, use the Associative and Distributive Properties to simplify the expressions. If radical expressions are not in simplest form, simplify them.

Example 1 Simplify 106 - 53 + 63 - 46. 106 - 53 + 63 - 46 = (10 - 4)6 + (-5 + 6)3

= 66 + 3

Associative and Distributive Properties Simplify.

Example 2 Simplify 312 + 575 .

312 + 575 = 322 ? 3 + 552 ? 3

Factor 12 and 75.

= 3 ? 23 + 5 ? 53

Simplify.

= 63 + 253

Multiply.

= 313

Distributive Property

Exercises

Simplify each expression.

1. 25 + 45 65

2. 6 - 46 -36

3. 8 - 2 2

4. 375 + 25 153 + 25

5. 20 + 25 - 35 5

6. 23 + 6 - 53 -33 + 6

7. 12 + 23 - 53 -3

8. 36 + 32 - 50 + 24 56 - 22

9. 8a - 2a + 52a 62a

10. 54 + 24 56

11. 3 + -31 - 433

12. 12 + -31 - 733

13. 54 -

-61

- 17 6 6

14. 80 - 20 + 180 85

15. 50 + 18 - 75 + 27 82 - 23 16. 23 - 445 + 2 -31 - 833 - 125

17. 125 - 2 -51 + -31 - 2355 + - 33

18. -23 + 33 - 4 - 112 - 6 +373

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 10-3

Chapter 10

17

Glencoe Algebra 1

NAME

DATE

PERIOD

10-3 Study Guide and Intervention (continued)

Operations with Radical Expressions

Multiply Radical Expressions Multiplying two radical expressions with different

radicands is similar to multiplying binomials.

Example Multiply (32 - 25)(4 20 + 8). Use the FOIL method.

(32 - 25)(420 + 8) = (32)(420) + (32)(8) + (-25)(420) + (-25)(8)

= 1240 + 316 - 8100 - 240 = 1222 ? 10 + 3 ? 4 - 8 ? 10 - 222 ? 10 = 2410 + 12 - 80 - 410 = 2010 - 68

Multiply. Simplify. Simplify. Combine like terms.

Exercises

Simplify each expression.

1. 2(3 + 45 ) 23 + 85

2. 6(3 - 26) 32 - 12

3. 5(5 - 2) 5 - 10

4. 2(37 + 25) 314 + 210

5. (2 - 42)(2 + 42) -28

6.

(3

+

) 2

6

15 + 66

( )2

7. 2 - 25

24 - 85

8. 32(8 + 24) 12 + 123

9. 8(2 + 58) 44

10. (5 - 32)(5 + 32) -13

( )2

11. 3 + 6

9 + 62

( )2

12. 2 - 23

14 - 46

13. (5 - 2)(2 + 6)

10 - 2 + 30 - 23

15. (5 - 18)(75 + 3)

35 + 15 - 2110 - 36

17. (25 - 23)(10 + 6)

42

14. (8 - 2)(3 + 6)

6 + 23

16. (23 - 45)(12 + 26)

12 - 615 + 122 - 630

18. (2 + 33)(12 - 48)

2 - 226

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 10

18

Glencoe Algebra 1

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