Surds

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Please change your TSR password 23-05-2013
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 20-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Sign in to Reply
  1. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Surds
    Hi, how do I rationalise this

    \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 - \sqrt 6}

    From the sum formula for tan I get as far as

    \displaystyle\dfrac{\frac{1}{4}(  \sqrt 2 + \sqrt 6)}{\frac{1}{4}(\sqrt 2 - \sqrt 6)}

    Then it's a mystery after cancelling the quarters.

    Maybe I should have worked out the tan values rather than going down the sin cos route?

    But it'd still be good to know what to do

    Maybe I am supposed to multiply the whole thing by \displaystyle\dfrac{\sqrt 2 - \sqrt 6}{\sqrt 2 - \sqrt 6} ?
    Last edited by SubAtomic; 23-07-2012 at 17:29.
  2. FrescoDiMorte's Avatar
    • Exalted Member
    • Location: London
    Re: Surds
    Multiply by \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6} I think.
  3. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    So I end up with

    \displaystyle\dfrac{-4}{8-2 \sqrt{12}}

    \displaystyle\dfrac{-4}{8-4 \sqrt 3}

    \displaystyle - \dfrac{1}{2-\sqrt 3}

    Am I doing this right? Sign error?
    Last edited by SubAtomic; 23-07-2012 at 17:41.
  4. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    Also could I suggest you buy a Casio Natural Display calculator as this will rationalise denominators for you?
  5. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Mr M)
    That step is correct. Rationalise again.
    \displaystyle - \dfrac{1}{2-\sqrt 3} ?
    Last edited by SubAtomic; 23-07-2012 at 17:46.
  6. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Mr M)
    Also could I suggest you buy a Casio Natural Display calculator as this will rationalise denominators for you?
    Yes I have one but am doing it by hand

    Good idea bad idea?
  7. Lord of the Flies's Avatar
    • The foul fiend Flibbertigibbet
    • Location: Paris, France
    Re: Surds
    (Original post by SubAtomic)
    Hi, how do I rationalise this

    \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 - \sqrt 6}

    From the sum formula for tan I get as far as

    \displaystyle\dfrac{\frac{1}{4}(  \sqrt 2 + \sqrt 6)}{\frac{1}{4}(\sqrt 2 - \sqrt 6)}

    Then it's a mystery after cancelling the quarters.

    Maybe I should have worked out the tan values rather than going down the sin cos route?

    But it'd still be good to know what to do

    Maybe I am supposed to multiply the whole thing by \displaystyle\dfrac{\sqrt 2 - \sqrt 6}{\sqrt 2 - \sqrt 6} ?
    Much quicker to multiply the whole thing by \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6}

    ...
  8. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    (Original post by Lord of the Flies)
    Much quicker to multiply the whole thing by \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6}

    ...
    Yes, I thought that was what he put in the first place after he edited!

    OP just use your calculator or revise rationalising denominators from your Core 1 textbook.
  9. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Lord of the Flies)
    Much quicker to multiply the whole thing by \displaystyle\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6}

    ...
    \displaystyle\left(\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6}\right) \cdot \left(\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 - \sqrt 6}\right)
  10. Lord of the Flies's Avatar
    • The foul fiend Flibbertigibbet
    • Location: Paris, France
    Re: Surds
    (Original post by SubAtomic)
    \displaystyle\left(\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 + \sqrt 6}\right) \cdot \left(\dfrac{\sqrt 2 + \sqrt 6}{\sqrt 2 - \sqrt 6}\right)
    Hum, yes?...
  11. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Mr M)
    Yes, I thought that was what he put in the first place after he edited!

    OP just use your calculator or revise rationalising denominators from your Core 1 textbook.
    Yeah I kinda forgot what I was doing until I typed it up, C1 Never did it, all OU maths.
  12. FrescoDiMorte's Avatar
    • Exalted Member
    • Location: London
    Re: Surds
    Thats what I said I think he should get

    8+4(root3)/ -4
  13. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Lord of the Flies)
    Hum, yes?...
    Wasn't questioning was just typing. Can see how that'd be the logical thing to do
  14. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    (Original post by SubAtomic)
    Yeah I kinda forgot what I was doing until I typed it up, C1 Never did it, all OU maths.
    Ok just go back and do it again.

    Use your knowledge of the difference of two squares (a+b)(a-b)=a^2-b^2 to reduce working.
  15. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    (Original post by FrescoDiMorte)
    Thats what I said I think he should get

    8+4(root3)/ -4
    Surely that simplies further?
  16. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Mr M)
    Surely that simplies further?
    Certainly does, -2 - \sqrt 3
  17. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    (Original post by SubAtomic)
    Certainly does, -2 - \sqrt 3
    which is the correct answer.

    Which OU module is this?
  18. FrescoDiMorte's Avatar
    • Exalted Member
    • Location: London
    Re: Surds
    (Original post by Mr M)
    Surely that simplies further?
    -2-root3/1
  19. SubAtomic's Avatar
    • Exalted and Worshipped Member
    • Posts: 1,316
    Re: Surds
    (Original post by Mr M)
    which is the correct answer.

    Which OU module is this?
    It is a part of MS221 on trig formulas, when I look in the back of the book it seems I went the long way around by using the sin cos vals instead of using tan vals straight away. No mention of whether to use a calculator or not, just assumed as per.

    Never did much with surds at GCSE, or at OU on 123 or 121, soon forget stuff if I don't keep up with the practice.

    Thanks people
    Last edited by SubAtomic; 23-07-2012 at 18:09.
  20. Mr M's Avatar
    • Community Assistant
    • TSR Royalty
    • Location: Suffolk
    • Posts: 18,169
    Re: Surds
    (Original post by SubAtomic)
    It is a part of MS221 on trig formulas, when I look in the back of the book it seems I went the long way around by using the sin cos vals instead of using tan vals straight away. No mention of whether to use a calculator or not, just assumed as per.
    My wife did that module a few years ago. You are allowed a calculator in the exam.
Sign in to Reply
Share this discussion:  
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.