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    I'm having difficulty with the following question:

    Express  \dfrac {8+ \sqrt 7} {2+ \sqrt 7} in the form  a+b \sqrt 7 , where a and b are integers.

    I'm sure it's something fairly simple, but looking over my notes I can't see a trace of a question set out like that.

    Thanks in advance,

    Digichris.
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    (Original post by Digichris)
    I'm having difficulty with the following question:

    Express  \dfrac {8+ \sqrt 7} {2+ \sqrt 7} in the form  a+b \sqrt 7 , where a and b are integers.

    I'm sure it's something fairly simple, but looking over my notes I can't see a trace of a question set out like that.

    Thanks in advance,

    Digichris.
    Multiply both the numerator and the denominator by  2-\sqrt7. This rationalises the denominator.
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    Method is called rationalising the denominator!
    Multiply the numerator and denominator by 2-(root 7) and simplify...
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    mulitply by the fraction

    2+?7/2+?7 and simplify

    hope that makes sense
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    The problem is that after that, it still needs to be in the correct form, and I can't seem to get it to do that.

    It's not just rationalising the denominator, it's also getting it into the correct form, which I'm having trouble with.
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    (Original post by Digichris)
    The problem is that after that, it still needs to be in the correct form, and I can't seem to get it to do that.

    It's not just rationalising the denominator, it's also getting it into the correct form, which I'm having trouble with.
    Once you've rationalised the denominator, gather the terms in the numerator that don't contain \sqrt7 and those that do. You should end up with something in the form of  \dfrac{x+y\sqrt7}{z} where x, y and z are constants. You can then rearrange this in the form \dfrac{x}{z}+\dfrac{y\sqrt7}{z} where x/z will be a and y/z will be b.

    Sorry if this explanation is confusing.
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    (Original post by Gemini92)
    Once you've rationalised the denominator, gather the terms in the numerator that don't contain \sqrt7 and those that do. You should end up with something in the form of  \dfrac{x+y\sqrt7}{z} where x, y and z are constants. You can then rearrange this in the form \dfrac{x}{z}+\dfrac{y\sqrt7}{z} where x/z will be a and y/z will be b.

    Sorry if this explanation is confusing.
    Excellent, thank you very much!
 
 
 
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Updated: March 26, 2011
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