The discussion revolves around determining the percentage of rational square roots of integers within specified ranges: 1 to 2000 and 1 to 10,000. Participants explore the nature of square roots and their rationality based on integer values.
The discussion is ongoing, with various interpretations being explored. Some participants have provided insights into counting perfect squares, while others express confusion about the calculations and definitions involved.
Participants note that calculators are not to be used, which may affect the methods of exploration. There is also a mention of disappointment regarding the clarity of responses and the accuracy of previous answers provided in the thread.
phospho said: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?
SammyS said:What is √(2000) ?
What is √(10,000) ?
Find the largest integer whose square is less than 2000 .phospho said:20√5 and 100, I don't see where you're going with this. Also no calculators are to be used for future reference
phospho said: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?
Ray Vickson said:If an integer does not have an integer square root, does it have a rational square root?
RGV
HallsofIvy said: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.
oh I see, so I how would I go about finding the percentage?SammyS said:Find the largest integer whose square is less than 2000 .
402 = 1600 .
502 = 2500 .
Look at 442 & 452 .
How many perfect square integers are there from 1 to 2000 ?phospho said:No
That's the whole question I have been given
oh I see, so I how would I go about finding the percentage?
SammyS said:How many perfect square integers are there from 1 to 2000 ?
How many integers are there from 1 to 2000 ?
phospho said:So 2.2 and 1%?
SammyS said:How many perfect square integers are there from 1 to 2000 ?
How many integers are there from 1 to 2000 ?
phospho said:So 2.2 and 1%?
Thanks Mark.Mark44 said:These are not the answers to the questions that Sammy asked.
Mark44 said:These are not the answers to the questions that Sammy asked.
SammyS said:Thanks Mark.
I was also disappointed with OP's response, even though he/she did finally solve the given problem.