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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Lecture Comments (2)

1 answer

Last reply by: Dr Carleen Eaton
Sun Jan 27, 2013 1:18 PM

Post by nikolin leskaj on January 27, 2013

1:20min distributive property a(b+c)=ab+cd , should be a(b+c)=ab+ac

Operations with Radical Expressions

  • When adding or subtracting, combine only like radicals.
  • To multiply one radical expression by another one, use the same techniques you have learned for multiplying one polynomial by another one.

Operations with Radical Expressions

Simplify:
3√7 + 8√5 − 9√7 − 6√5
  • ( 3√7 − 9√7 ) + ( 8√5 − 6√5 )
− 6√7 + 2√5
Simplify:
4√{11} − 20√3 − 16√{11} − 5√3
  • ( 4√{11} − 16√{11} ) + ( 20√3 − 5√3 )
− 12√{11} − 25√3
Simplify:
64√{17} − 12√2 − 23√2 + 15√{17}
  • ( 64√{17} − 15√{17} ) + ( 12√2 − 23√2 )
79√{17} − 35√2
Simplify:
3√{12x} + 4√{27x} − 5√{3x} + 6√{75x}
  • 3√4 ×√{3x} + 4√9 ×√{3x} − 5√1 ×√{3x} + 6√{25} ×√{3x}
  • 3 ×2√{3x} + 4 ×3√{3x} − 5 ×1√{3x} + 6 ×5√{3x}
  • 6√{3x} + 12√{3x} − 5√{3x} + 30√{3x}
43√{3x}
Simplify:
7√{32y} − 8√{72y} + 4√{98y} + 6√{200y}
  • 7√{16} ×√{2y} − 8√{36} ×√{2y} + 4√{49} ×√{2y} + 6√{100} ×√{2y}
  • 7 ×4√{2y} − 8 ×6√{2y} + 4 ×7√{2y} + 6 ×10√{2y}
  • 28√{2y} − 48√{2y} + 28√{2y} + 60√{2y}
68√{2y}
Simplify:
5√{196n} − 3√{256n} − 2√{324n} + 8√{36n}
  • 5√{49} ×√{4n} − 3√{64} ×√{4n} − 2√{81} ×√{4n} + 8√9 ×√{4n}
  • 5 ×7√{4n} − 3 ×8√{4n} − 2 ×9√{4n} + 8 ×3√{4n}
17√{4n}
Simplify:
( 4√3 − 6√5 )2
  • ( a − 6 )2 = a2 − 2ab + b2
  • ( 4√3 )2 − 2( 4√3 )( 6√5 ) + ( 6√5 )2
  • 16 ×3 − ( 2 )( 4 )( 6 )√3 √5 + 36 ×5
  • 48 − 48√{3 ×5} + 180
228 − 48√{15}
Simplify:
( 2√7 − 3√{11} )2
  • ( 2√7 )2 − 2( 2√7 )( 3√{11} ) + ( 3√{11} )2
  • 4 ×7 − 2( 2 )( 3 )√7 √{11} + 9 ×11
  • 28 − 12√{7 ×11} + 99
127 − 12√{77}
Simplify:
( 2√{10} − 4√{12} )( 3√{15} − 5√5 )
  • ( 2√{10} )( 3√{15} ) + ( 2√{10} )( − 5√5 ) + ( − 4√{12} )( 3√{15} ) + ( − 4√{12} )( − 5√5 )
  • 6√{10} √{15} − 10√{10} √5 − 12√{12} √{15} + 20√{12} √5
  • 6√{150} − 10√{50} − 12√{180} + 20√{60}
  • 6√{25 ×6} − 10√{25 ×2} − 12√{9 ×4 ×5} + 20√{4 ×15}
  • 6 ×5√6 − 10 ×5√2 − 12 ×3 ×2√5 + 20 ×2√{15}
30√6 − 50√2 − 72√5 + 40√{15}
Simplify:
( 6√{40} + 7√{24} )( 10√{18} − 12√{30} )
  • ( 6√{40} )( 10√{18} ) + ( 6√{40} )( − 12√{30} ) + ( 7√{24} )( 10√{18} + ) + ( 7√{24} )( − 12√{30} )
  • 60√{720} − 72√{1200} + 70√{432} − 84√{720}
  • 60√{9 ×16 ×5} − 72√{100 ×4 ×3} + 70√{16 ×9 ×3} − 84√{9 ×16 ×5}
  • 60 ×3 ×4√5 − 72 ×10 ×2√3 + 70 ×4 ×3√3 − 84 ×3 ×4√5
  • 720√5 − 1440√3 + 840√3 − 1008√5
− 288√5 − 600√3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Operations with Radical Expressions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Adding and Subtracting Radical Expressions 0:13
    • Like Radicals
    • Distributive Property
  • Multiplying Radical Expressions 4:24
    • Example: Use FOIL
  • Example 1: Simplify Expression 7:07
  • Example 2: Simplify Expression 8:51
  • Example 3: Simplify Expression 12:14
  • Example 4: Simplify Expression 16:06