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Math Help - Surds...

  1. #1
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    Surds...

    (√a+√b)=a+b+2√ab

    determine the square root of 17+6√8


    I hope you can help,
    thanks.
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  2. #2
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    Quote Originally Posted by glenn101 View Post
    (√a+√b)=a+b+2√ab

    determine the square root of 17+6√8


    I hope you can help,
    thanks.
    A square root of a+b+2√ab is clearly √a+√b.

    Note that 17 + 6√8 = 17 + 2√(9)(8) = 17 + 2√72.

    Compare with a+b+2√ab.

    Therefore solve the following two equations simultaneously:

    a + b = 17 ... (1)
    ab = 72 ... (2)

    I get a = 9 and b = 8 (and obviously the other solution is a = 8 and b = 9) ......

    Then a square root of 17+6√8 is √a+√b = ......
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