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Math Help - Adding and Subtracting Radicals with Different Radicands

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    Adding and Subtracting Radicals with Different Radicands

    I get confused only at the very end of this problem...I got the answer from the book:
    (*= radical sign)

    = 5 *3 - 2 *3
    =(5 - 2) *3
    = 3 *3

    My question is: where does the other *3 go? Why is there only one *3 in the final answer?
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    5\sqrt{3} - 2\sqrt{3} = 3\sqrt{3}

    Imagine a = \sqrt{3}: 5a - 2a = 3a
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    Quote Originally Posted by endlesst0m View Post
    My question is: where does the other *3 go? Why is there only one *3 in the final answer?
    The answer is: it's still there! You start off with two square roots of three being subtracted from five square roots of three. You are then left with three square roots of three, because 5 of something minus 3 of something is 2 of that something.

    There may only be one radical in the final answer, but it is being multiplied by three, which is the same as adding it to itself twice.
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