Results 1 to 6 of 6

Math Help - Year 8 maths. quick

  1. #1
    Banned
    Joined
    Jun 2008
    Posts
    4

    Exclamation Year 8 maths. quick

    This is again urgent maths hw. please help me. thx

    Find all three-digit even numbers N such that 693 x N is a perfect square, that is, 693 x N = k to the power of 2 where k is an integer


    i am in yr 8. please explain in easy words...:P but answer it completly (i know im mean but wat u have dun will work) thx!


    i get it and how it works but how did u get 693 = the factors 7,3,11. how did u get those 3 numbers?
    Last edited by claudeluvstwilight; June 27th 2008 at 04:40 AM. Reason: help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by claudeluvstwilight View Post
    This is again urgent maths hw. please help me. thx

    Find all three-digit even numbers N such that 693 x N is a perfect square, that is, 693 x N = k to the power of 2 where k is an integer
    693 = 3^2 \cdot 7 \cdot 11

    So any number we multiply this by to make a perfect square has to contain factors of 7 and 11. Since this number has to be even as well, it needs to contain a 4 = 2^2.

    The smallest N that qualifies is 308. I leave it to you to find the rest (if any).

    Hint: What is the smallest number you can multiply this by and still leave the product a perfect square?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello

    Quote Originally Posted by claudeluvstwilight View Post
    This is again urgent maths hw. please help me. thx

    Find all three-digit even numbers N such that 693 x N is a perfect square, that is, 693 x N = k to the power of 2 where k is an integer
    693=63*11=7*9*11=7^1*3^2*11^1.

    A perfect square is formed by the product of numbers to an even power.

    So here, you have to multiply 693 by a number that will yield even powers of 7, 3, 11 in the product.


    7^1 \rightarrow \text{multiply by {\color{red}7}} \rightarrow 7^2

    3^2 \rightarrow \text{OK.}

    11^1 \rightarrow \text{multiply by {\color{red}11}} \rightarrow 11^2


    --> N=7*11=77

    Multiply N by all perfect squares, until you don't have 3-digit numbers anymore.

    4*77=\boxed{308} \rightarrow \text{OK.}
    9*77=\boxed{693} \rightarrow \text{OK.}
    16*77=1232 \rightarrow \text{not OK.}

    Is it clear enough ?
    Last edited by Moo; June 27th 2008 at 04:29 AM. Reason: typo >.<
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,842
    Thanks
    320
    Awards
    1
    Quote Originally Posted by Moo View Post
    Hello



    693=63*11=7*9*11=7^1*3^2*11^1.

    A perfect square is formed by the product of numbers to an even power.

    So here, you have to multiply 693 by a number that will yield even powers of 7, 9, 11 in the product.


    7^1 \rightarrow \text{multiply by {\color{red}7}} \rightarrow 7^2

    3^2 \rightarrow \text{OK.}

    11^1 \rightarrow \text{multiply by {\color{red}11}} \rightarrow 11^2


    --> N=7*11=77
    But 9 is 3 squared.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by topsquark View Post
    But 9 is 3 squared.

    -Dan
    I edited some things in my rush
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2008
    Posts
    4
    Intereted in this one, does that mean tht 308 isthe only possible answer? How do we know for sure because it has to be even.

    wasn't it stated that it must be divsible by 3 and to get perfect square you must times all the number by the same thing. E.g. 11 sqauredx 7 squared x 3 squared?

    im confused
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 16th 2010, 02:39 PM
  2. Year 9 maths homework extension
    Posted in the Algebra Forum
    Replies: 14
    Last Post: February 2nd 2009, 09:37 AM
  3. Replies: 5
    Last Post: January 2nd 2009, 02:58 AM
  4. [SOLVED] Year 8 maths. quick
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 27th 2008, 06:48 AM
  5. maths year six
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 22nd 2007, 11:15 AM

Search Tags


/mathhelpforum @mathhelpforum