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Math Help - Multiplying Radicals

  1. #1
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    Multiplying Radicals

    Stuck on a problem that I solved but doesnt look right to me for some reason.

    Perform the indicated operation and simplify:

    (2 √5 - 4 √6)(3 √3 + 8 √2)

    So I used FOIL to expand.. not sure if people are familiar with the term (first term, outside/inside term, last term) and got.

    (2 x 3)(√5 x √3) + (2 x 8)(√5 x √2) + (-4 x 3)(√6 x √3) + (-4 x 8)(√6 x √2)

    Then simplified √18 and √12 further

    6√15 + 16√10 - 12(3√2) - 32(2√3)

    = 6√15 + 16√10 -36√2 - 64√3

    .. Problem is I never learned a way to check your answer, if there is even one. Any clarification would greatly be appreciated.
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  2. #2
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    It looks correct.
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  3. #3
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    Thanks, Steve.
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  4. #4
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    Quote Originally Posted by danzig View Post
    Perform the indicated operation and simplify:

    (2 √5 - 4 √6)(3 √3 + 8 √2)

    So I used FOIL to expand.. not sure if people are familiar with the term (first term, outside/inside term, last term) and got.

    (2 x 3)(√5 x √3) + (2 x 8)(√5 x √2) + (-4 x 3)(√6 x √3) + (-4 x 8)(√6 x √2)

    Then simplified √18 and √12 further

    6√15 + 16√10 - 12(3√2) - 32(2√3)

    = 6√15 + 16√10 -36√2 - 64√3

    .. Problem is I never learned a way to check your answer, if there is even one. Any clarification would greatly be appreciated.
    Your answer is correct; to check, simply use calculator:

    Initial expression: (2 √5 - 4 √6)(3 √3 + 8 √2) = -87.928597...

    Your solution: 6√15 + 16√10 -36√2 - 64√3 = -87.928597...

    NOTE: I meant your solution is correct mathematically;
    I don't know the "format" your teacher expects.
    Like: 2(3√15 + 8√10 -18√2 - 32√3) ?
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