Hey there! Sign in to join this conversationNew here? Join for free

C1 surds question Watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:






    As you can see my working too much longer, I don't understand their method but I want to learn their method cause it seems much simpler.

    Q1) So can somone please explain each step in their method to me?

    Q2) What I don't understand is why they havent multiped the numerator and denomintor of 12/48 by the root of 48? The book stated "Fractions in the form 1/root of a, multiply the top and bottom by root of a."

    So can you please anwer my two questions.

    Thanks
    Offline

    1
    ReputationRep:
    Root 48 = Root 12 * Root 4
    That is a fact which you should know.
    [Root a * Root b] = Root (ab)
    This means that you get (Root 12)/(Root 12 *Root 4)
    Now you can divide Top and Bottom by root 12 to get 1/(Root 4) Is it this bit that you don't understand?
    As Root 4 = 2 then 1/ (Root 4) = 1/2


    The reason that they haven't multiplied by Root 48 is because it is quicker their way. If you ever get a question like this again e.g. Root a / Root b always try and write it in the form Root a / (Root a * Root c) where c = b/a

    Geddit?
    Offline

    0
    ReputationRep:
    I got about halfway through explaining how they did it and realised I don't really know :confused: lol

    they think (route 12) divided by (route 12) is 1, which it is, but I thought if you have two surds like that you just cancel them out? But then you would end up with nothing over (route 4)

    Although their method may look simpler on that question, it is easier just to use the method you used

    Sorry for the lack of help
    Offline

    1
    ReputationRep:
    (Original post by ChocolateWar)
    I got about halfway through explaining how they did it and realised I don't really know :confused: lol

    they think (route 12) divided by (route 12) is 1, which it is, but I thought if you have two surds like that you just cancel them out? But then you would end up with nothing over (route 4)

    Although their method may look simpler on that question, it is easier just to use the method you used

    Sorry for the lack of help
    Their method IS simpler if you can spot the factors (which is really quite easy tbh.) If you spot the factors then you don't have to do as much tedious multiplication
    • Thread Starter
    Offline

    1
    ReputationRep:
    I the bit i dont get is why not multiply the numerator and denom by root of 48. after all this is the method the books says to follow "Fractions in the form 1/root of a, multiply the top and bottom by root of a.".

    they seem to be doing something different alltogether
    Offline

    2
    ReputationRep:


    You can split up numbers under a square root sign into its factors multiplied by each other, for example:

    \sqrt{6} = \sqrt{2 \times 3} = \sqrt{2} \times \sqrt{3}

    The person who did the working out in your OP noticed that 12 is a factor of 48, and decided to use this knowledge to his advantage. Note that you broke down 48 into lots of very low factors whereas this person saw that getting a factor of 12 would do.



    So,

    \frac{\sqrt{12}}{\sqrt{48}} = \frac{\sqrt{12} \times 1}{\sqrt{12} \times \sqrt{4}}




    If you had \frac{4}{12} you would cancel it down to \frac{1}{3} because you can see that 4 is a factor of the numerator and denominator (ie, it is "in" both of them so you can cancel it out: \frac{4}{12} = \frac{1 \times 4}{3 \times 4} )

    We have already shown above that \sqrt{12} is a factor of the numerator and denominator in our example, so we can cancel ours down to \frac{1}{\sqrt{4}} = \frac{1}{2}.

    Remember that anything divided by itself equals 1, which is where the 1 comes from. And we know what the square root of 4 is, which is 2.




    To your second question, you can do it your way/the book's way too. Both are valid - all they are doing is rewriting it a different way so it's easier to see what you can cancel out in the fractions.
    • Thread Starter
    Offline

    1
    ReputationRep:
    ok fine but if i was to use their method for this question id get it wrong



    ????????? SO CONFUSED!!!
    Offline

    0
    ReputationRep:
    (Original post by jayseanfan)
    ok fine but if i was to use their method for this question id get it wrong



    ????????? SO CONFUSED!!!
    The whole point of rationalising the denominator is to not have a surd as a denominator. The way its been simplified above is correct, but its not simplified fully, as you've ended up with \dfrac{1}{\sqrt 5}. Rationalise this again, and you get \dfrac{\sqrt 5}{5}.

    In simple terms:

    

\dfrac{1}{\sqrt 5} = \dfrac{\sqrt 5}{5}
    Offline

    0
    ReputationRep:
    (Original post by jayseanfan)
    ok fine but if i was to use their method for this question id get it wrong



    ????????? SO CONFUSED!!!
    your ansewer and theirs are the same thing, but in yours you haven't rationalised the denominator. Rationalising means to get the surds off the denominator, so multiply your answer by root5/root5 and you get theirs.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.