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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