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

Stumped on a Q Watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12
    Offline

    0
    ReputationRep:
    Huh????? :confused:
    • Community Assistant
    Offline

    19
    ReputationRep:
    17\sqrt{1-\frac{1}{17^2}}=\sqrt{17^2-1}

    There you go!
    Offline

    16
    ReputationRep:
    17^2 = 289

    So you have root(288)
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by McLH)
    Sqrting the individual terms
    The answer that \sqrt{a^2+b^2}=a+b is horrendous.

    This suggests that 5=\sqrt{3^2+4^2}=3+4=7
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr M)
    The answer that \sqrt{a^2+b^2}=a+b is horrendous.

    This suggests that 5=\sqrt{3^2+4^2}=3+4=7
    I know, tis why I said I knew it was wrong
    Offline

    0
    ReputationRep:
    What?! How do you guys do this!? :confused:
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by Bexsqueak)
    What?! How do you guys do this!? :confused:
    How do we do what?
    Offline

    0
    ReputationRep:
    (Original post by McLH)
    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12
    17 \times \sqrt{1 - \frac{1}{17^{2}}} = 17 \times \dfrac{\sqrt{17^{2} - 1}}{17} = \sqrt{17^{2} - 1}
    • Study Helper
    Offline

    16
    ReputationRep:
    (Original post by McLH)
    Show that 17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\s  qrt{2}, when n is an integer, whose value is to be found.

    I can't see how to do this without sqrting an "unfinished" bracket:

    17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}

    Sqrting the individual terms (I know is wrong) but would give  17(1-17^{-1}) = 16 .

    Any clues would be greatly appreciated

    *The answer booklet says n = 12

    (Original post by Bexsqueak)
    What?! How do you guys do this!? :confused:
    Take the 17 inside the bracket (squaring it, as others have shown), then use difference of 2 squares to factorize what is now inside the brackets
 
 
 
  • 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.