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Math Help - Rationalize the denominator

  1. #1
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    Rationalize the denominator

    I need help with this:

    Rationalize the denominator:

    Thanks in advance
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  2. #2
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    Quote Originally Posted by Cuelguy View Post
    I need help with this:

    Rationalize the denominator:

    sqrt{6}+sqrt{5}/sqrt{6}-sqrt{5}

    Thanks in advance.
    Are you familiar with "the difference of two squares", basically it says that:
    a^2-b^2=(a-b)(a+b)
    now with this in mind think about what you might like to multiply the numerator and denominator of your fraction by...
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  3. #3
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    Quote Originally Posted by pfarnall View Post
    Are you familiar with "the difference of two squares", basically it says that:
    a^2-b^2=(a-b)(a+b)
    now with this in mind think about what you might like to multiply the numerator and denominator of your fraction by...
    ....the conjugate of the denominator, correct?

    So I would multiply the numerator and denominator by sqrt(6) + sqrt(5) ?
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  4. #4
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    Quote Originally Posted by Cuelguy View Post
    ....the conjugate of the denominator, correct?

    So I would multiply the numerator and denominator by sqrt(6) + sqrt(5) ?
    Spot on! Well done, and the formula I gave you means you don't even have to work out what the new denominator will be, it's already there for you!
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  5. #5
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    Quote Originally Posted by pfarnall View Post
    Spot on! Well done, and the formula I gave you means you don't even have to work out what the new denominator will be, it's already there for you!
    Okay here is what I got as a final answer after collecting all the like terms, but the answer is still wrong. I am pretty sure it's because of the square root of 5 & 6 in my answer below....I don't know how to combine them.
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  6. #6
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    \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}-\sqrt{5}} \cdot \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}} = \frac{6 + 2\sqrt{30} + 5}{6 - 5} = 11 + 2\sqrt{30}
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  7. #7
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    Yes you had it all, you just need to learn that \sqrt{a}\sqrt{b}=\sqrt{ab} (also that 6-5=1 but I'm sure you know that already)
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