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Percentage of √n

  1. Jul 29, 2012 #1
    What percentage of √n, where n E Z (n is an element of integers), are rational, where

    a) 1 ≤ n ≤ 2000.

    b) 1 ≤ n ≤ 10,000.

    No idea how to go about this, any help?
     
  2. jcsd
  3. Jul 29, 2012 #2

    SammyS

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    What is √(2000) ?

    What is √(10,000) ?
     
  4. Jul 29, 2012 #3
    20√5 and 100, I don't see where you're going with this. Also no calculators are to be used for future reference
     
  5. Jul 29, 2012 #4

    SammyS

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    Find the largest integer whose square is less than 2000 .

    402 = 1600 .

    502 = 2500 .

    Look at 442 & 452 .
     
  6. Jul 29, 2012 #5

    HallsofIvy

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    Before you can ask "What percentage of √n, where n E Z (n is an element of integers), are rational" you have to specify a measure on the set of integers. To find a percentage you have to have a ratio and to have a ratio here you need a size for each set.
     
  7. Jul 29, 2012 #6

    Ray Vickson

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    If an integer does not have an integer square root, does it have a rational square root?

    RGV
     
  8. Jul 29, 2012 #7
    No

    That's the whole question I have been given

    oh I see, so I how would I go about finding the percentage?
     
  9. Jul 29, 2012 #8

    SammyS

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    How many perfect square integers are there from 1 to 2000 ?

    How many integers are there from 1 to 2000 ?
     
  10. Jul 30, 2012 #9
    So 2.2 and 1%?
     
  11. Jul 30, 2012 #10

    Mentallic

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    Yep.
     
  12. Jul 30, 2012 #11

    Mark44

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    These are not the answers to the questions that Sammy asked.
     
  13. Jul 30, 2012 #12

    SammyS

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    Thanks Mark.

    I was also disappointed with OP's response, even though he/she did finally solve the given problem.
     
  14. Jul 30, 2012 #13
    Sorry to disappoint didn't really want to waste much more of your time as I got the answer,

    How many perfect square integers are there from 1 to 2000 ? 44

    How many integers are there from 1 to 2000 ? 2000

    thank you again.
     
  15. Jul 30, 2012 #14

    Mark44

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    Thanks for clarifying this, phospho. The reason for my comment was that a member might read this thread, and wonder how you determined that there were 2.2 perfect squares in the first 2000 integers.
     
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