Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

expand (4+3√2)^2?

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

7 Answers

Relevance
  • ?
    Lv 7
    1 month 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

  • ?
    Lv 7
    1 month ago

    [4+3sqr(2)]^2

    =

    16+24sqr(2)+18

    =

    34+24sqr(2)

    =>

    a=34

    b=24

  • 1 month 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//

  • ?
    Lv 7
    1 month ago

    (4 + 3√2)^2 = 34 + 24√2

  • How do you think about the answers? You can sign in to vote the answer.
  • 1 month 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

  • 1 month 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

  • ?
    Lv 7
    1 month ago

    It is: 18 + 8 times square root 2

Still have questions? Get your answers by asking now.