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    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12
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    Huh????? :confused:
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    17\sqrt{1-\frac{1}{17^2}}=\sqrt{17^2-1}

    There you go!
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    17^2 = 289

    So you have root(288)
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    (Original post by McLH)
    Sqrting the individual terms
    The answer that \sqrt{a^2+b^2}=a+b is horrendous.

    This suggests that 5=\sqrt{3^2+4^2}=3+4=7
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    (Original post by Mr M)
    The answer that \sqrt{a^2+b^2}=a+b is horrendous.

    This suggests that 5=\sqrt{3^2+4^2}=3+4=7
    I know, tis why I said I knew it was wrong
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    What?! How do you guys do this!? :confused:
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    (Original post by Bexsqueak)
    What?! How do you guys do this!? :confused:
    How do we do what?
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    (Original post by McLH)
    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12
    17 \times \sqrt{1 - \frac{1}{17^{2}}} = 17 \times \dfrac{\sqrt{17^{2} - 1}}{17} = \sqrt{17^{2} - 1}
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    (Original post by McLH)
    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12

    (Original post by Bexsqueak)
    What?! How do you guys do this!? :confused:
    Take the 17 inside the bracket (squaring it, as others have shown), then use difference of 2 squares to factorize what is now inside the brackets
 
 
 
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