5.4 The Irrational Numbers 253 Multiplication of Radicals When multiplying radicals, we again make use of the product rule for radicals, as introduced earlier. After the radicands are multiplied, simplify the remaining radical when possible. Example 3 Subtracting Radicals with Different Radicands Simplify 6 2 18. − Solution When two square roots have different radicands, they cannot be added or subtracted. When this occurs, we should try to simplify one or both square roots. If the simplified square roots have the same radicand, then we can perform addition or subtraction. 6 2 18 6 2 9 2 6 2 9 2 6 2 3 2 (6 3) 2 3 2 − = − ⋅ = − ⋅ = − = − = 7 Now try Exercise 49 Example 4 Multiplying Radicals Simplify. a) 3 12 ⋅ b) 2 15 ⋅ c) 2 28 ⋅ Solution a) 3 12 312 36 6 ⋅ = ⋅ = = b) 2 15 215 30 ⋅ = ⋅ = c) 2 28 228 56 414 4 14 214 ⋅ = ⋅ = = ⋅ = ⋅ = 7 Now try Exercise 53 Division of Radicals To divide radicals, use the following rule. After performing the division, simplify when possible. Quotient Rule for Radicals = ≥ > a b a b a b , 0, 0 Learning Catalytics Keyword: Angel-SOM-5.4 (See Preface for additional details.) Example 5 Dividing Radicals Divide. a) 50 2 b) 90 5 Solution a) 50 2 50 2 25 5 = = = b) 90 5 90 5 18 9 2 9 2 3 2 = = = ⋅ = ⋅ = 7 Now try Exercise 57
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