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Module 13

Simplifying, Adding, Subtracting, and Multiplying Radical Expressions

QuestionAnswer
4√11 + 8√11= 4√11 + 8√11= (4+8)√11 = 12√11
(5)³√3x - (7)³√3x = (5)³√3x - (7)³√3x= (5-7)³√3x = -2³√3x
2√7 + 2³√7 = 2√7 + 2³√7 This expression cannot be simplified since 2√7 and 2³√7 do not contain like radicals.
√20 + 2√45 = √20 + 2√45 = √4*5 + 2√9*5 =√4*√5 + 2*√9*√5 =2*√5 + 2*3*√5 =2√5 + 6√5 =8√5
³√54 - 5³√16 + ³√2 = ³√54 - 5³√16 + ³√2 = =³√27*³√2 - 5*³√8*³√2 + ³√2 =3*³√2 - 5*2*³√2 + ³√2 =3³√2 - 10³√2 + ³√2 =-6³√2
√45/4 - √5/3 = √45/4 - √5/3 = 3√5/4 - √5/3 =3√5*3/4*3 - √5*4/3*4 =9√5/12 - 4√5/12 =5√5/12
√3(5 + √30)= √3(5 + √30)= √3(5) + √3(√30) =5√3 + √3*30 =5√3 + √3*3*10 =5√3 + 3√10
(√5 - √6)(√7 + 1) = (√5 - √6)(√7 + 1) = To multiply, use the FOIL method √5*√7 + √5*1 - √6*√7 - √6*1 =√35 + √5 - √42 - √6
(4√3 - 1)² = (4√3 - 1)² = (4√3 - 1)(4√3 -1) =4√3(4√3)- 4√3(1) - 1(-1) =16*3 - 4√3 - 4√3 + 1 =48 - 8√3 + 1 =49-8√3
Created by: 580020310
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