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expand (4+3√2)^2?

give your answer in the form a + b √2  where a and b are integers

7 Answers

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  • Jim
    Lv 7
    2 months ago

    Use FOIL (a+b)(c+d) = ac+ad+bc+bd

    (4+3√2)(4+3√2) = 16 + 12√2 + 12√2 +9*2

    add like items

    34 + 24√2

  • 2 months ago

    [4+3sqr(2)]^2

    =

    16+24sqr(2)+18

    =

    34+24sqr(2)

    =>

    a=34

    b=24

  • 2 months ago

    (4+3√2)^2

    =(4+3√2)(4+3√2)

    =16 + 12√(2) + 12√(2) + 9√(4)

    =16 + 24√(2) + 9 * 2

    =16 + 24√(2) + 18

    =34 +  24√(2)   Answer//

  • 2 months ago

    (4 + 3√2)^2 = 34 + 24√2

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  • 2 months ago

    It's the same as this general form:

    (x + y)² = x² + 2xy + y²

    where:

    x = 4

    y = 3√2

    So this turns into:

    (4 + 3√2)² = 4² + 2(4)(3√2) + (3√2)²

    Now simplify the right side:

    (4 + 3√2)² = 16 + 24√2 + 9 * 2

    (4 + 3√2)² = 16 + 24√2 + 18

    (4 + 3√2)² = 34 + 24√2

    Testing both sides by using √2 = 1.41421:

    (4 + 3√2)² = 34 + 24√2

    (4 + 3 * 1.41421)² = 34 + 24 * 1.41421

    (4 + 4.24263)² = 34 + 33.94104

    8.24263² = 67.94104

    67.9409493169 = 67.94104

    round each to 5SF to get:

    67.941 = 67.941

    TRUE

    So this is correct.  The simplified expansion is:

    (4 + 3√2)² = 34 + 24√2

  • 2 months ago

    = (4 + 3√2)² → recall: (a + b)² = a² + 2ab + b²

    = (4)² + 2.(4 * 3√2) + (3√2)²

    = 16 + 24√2 + 18

    = 34 + 24√2

  • David
    Lv 7
    2 months ago

    It is: 18 + 8 times square root 2

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