Section 9.1Properties of Radicals 485Exercises9.1Dynamic Solutionsavailable at BigIdeasMath.comIn Exercises 5–12, determine whether the expression is in simplest form. If the expression is not in simplest form, explain why.5. √— 19 6. — 1 — 7 7.√— 48 8. √— 34 9. 5 — √— 2 10. 3 √— 10 — 4 11.1 — 2 + 3 √— 2 12. 6 3 √— 54 In Exercises 13–20, simplify the expression. (See Example 1.)13.√— 20 14. √— 32 15.√— 128 16. √— 72 17.√— 125b 18. √— 4x2 19. √— 81m3 20. √—48n5 In Exercises 21–28, simplify the expression. (See Example 2.)21. — 4 — 49 22. — 7 — 81 23. — 23 — 64 24. — 65 — 121 25. — a3 — 49 26. — 144 — k2 27.— 100 — 4x2 28. — 25v2 — 36 In Exercises 29–36, simplify the expression. (See Example 3.)29. 3 √— 16 30. 3 √— 108 31. 3 √— 64x532. 3 √— 343n2 33. 3 — 6c — 125 34. 3 — 8h4 — 27 35. 3 — 81y2 — 1000x3 36. 3 — 21 — 64a3b6 ERROR ANALYSIS In Exercises 37 and 38, describe and correct the error in simplifying the expression.37. √ — 72 = √ — 4 ⋅ 18 = √ — 4 ⋅ √ — 18 = 2 √ — 18 ✗
38. 3 — 128y3 — 125 3 √— 128y3 — 125 3 √—
64 ⋅ 2 ⋅ y3
——
125 3 √— 64 ⋅ 3 √— 2 ⋅ 3 √— y3 ——
125 4y 3 √— 2 — 125 ✗
Monitoring Progress and Modeling with MathematicsMonitoring Progress and Modeling with Mathematics 1. COMPLETE THE SENTENCE The process of eliminating a radical from the denominator of a radical expression is called _______________. 2. VOCABULARY What is the conjugate of the binomial √— 6 + 4? 3. WRITING Are the expressions 1 — 3 √— 2x and — 2x — 9equivalent? Explain your reasoning. 4. WHICH ONE DOESN’T BELONG? Which expression does not belong with the other three? Explain your reasoning.3 √— 3 1 — 3 √— 6 1 — 6 √— 6 3 √— 3 Vocabulary and Core Concept CheckVocabularyand Core ConceptCheck