Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

    i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

    so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

    can any of you illustrate that last step for me please
    Offline

    16
    ReputationRep:
    (Original post by Henry27)
    hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

    i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

    so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

    can any of you illustrate that last step for me please
    Please, post your workings.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Henry27)
    hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

    i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

    so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

    can any of you illustrate that last step for me please
    From there you could rationalise.

    But the easiest way to do this is to start again and use the fact that \displaystyle \frac{1}{8} = \frac{1}{2} \times \frac{1}{4}
    Offline

    22
    ReputationRep:
    (Original post by Henry27)
    hi so im kicking myself because i know this question is easy but im just not getting it, i have searched for help and what i have found has just confused me further.

    i need to express root 1/2 + root 1/4 + root 1/8 as a + b root c

    so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me

    can any of you illustrate that last step for me please
    So we have \displaystyle \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{2}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}

    This is akin to when we have \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} - common denominators.

    Back to the point: we have \displaystyle \frac{3}{2\sqrt{2}} we want to rationalise this, so we'll multiply top and bottom by \sqrt{2} to get us:

    \displaystyle \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2\sqrt{2}\sqrt{  2}} = \frac{3\sqrt{2}}{2\times 2}
    Offline

    22
    ReputationRep:
    (Original post by notnek)
    From there you could rationalise.

    But the easiest way to do this is to start again and use the fact that \displaystyle \frac{1}{8} = \frac{1}{2} \times \frac{1}{4}
    Isn't that what he's done? It's how he got \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}, isn't it? I can't quite see a simpler way except to pull out a factor of \frac{1}{\sqrt{2}}.
    Offline

    1
    ReputationRep:
    How can I put the numbers like that?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Zacken)
    Isn't that what he's done? It's how he got \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}}, isn't it? I can't quite see a simpler way except to pull out a factor of \frac{1}{\sqrt{2}}.
    It's easy to show \sqrt{\frac{1}{8}} = \frac{1}{2}\sqrt{\frac{1}{2}}

    And then simplify to get it in the form a + b root c.
    Offline

    22
    ReputationRep:
    (Original post by notnek)
    It's easy to show \sqrt{\frac{1}{8}} = \frac{1}{2}\sqrt{\frac{1}{2}}

    And then simplify to get it in the form a + b root c.

    That's what he's done though - if I'm not mistaken.

    (Original post by Henry27)
    so far i have gotten to 1/root 2 + 1/2 + 1/(2 root 2) but the process of turning 1/root 2 + 1/(2 root 2) into 3/4 root 2 is evading me
    It's inconsequential anyway, nevermind. :lol:
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    So we have \displaystyle \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{2}{2\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}

    This is akin to when we have \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} - common denominators.

    Back to the point: we have \displaystyle \frac{3}{2\sqrt{2}} we want to rationalise this, so we'll multiply top and bottom by \sqrt{2} to get us:

    \displaystyle \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2\sqrt{2}\sqrt{  2}} = \frac{3\sqrt{2}}{2\times 2}
    that is absolutely perfect, in fact now i see it i cant actually work out where i was going wrong haha.

    thanks for the help guys.
    Offline

    22
    ReputationRep:
    (Original post by Henry27)
    that is absolutely perfect, in fact now i see it i cant actually work out where i was going wrong haha.

    thanks for the help guys.
    Glad it helped!
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Zacken)
    That's what he's done though - if I'm not mistaken.



    It's inconsequential anyway, nevermind. :lol:
    I assumed a + b root c meant for any a, b, c - the question wasn't clear. Then rationalising would be unnecessary.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 15, 2016
The home of Results and Clearing

2,888

people online now

1,567,000

students helped last year

University open days

  1. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  2. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
  3. University of Glasgow
    All Subjects Undergraduate
    Tue, 28 Aug '18
Poll
How are you feeling about GCSE results day?
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.