Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    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.
    Offline

    0
    ReputationRep:
    (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.
    Offline

    6
    ReputationRep:
    Method is called rationalising the denominator!
    Multiply the numerator and denominator by 2-(root 7) and simplify...
    Offline

    1
    ReputationRep:
    mulitply by the fraction

    2+?7/2+?7 and simplify

    hope that makes sense
    • Thread Starter
    Offline

    0
    ReputationRep:
    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.
    Offline

    0
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (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!
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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

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

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