What percentage of square roots are rational for 1 ≤ n ≤ 2000 and 1 ≤ n ≤ 10,000?

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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?
 
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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?


What is √(2000) ?

What is √(10,000) ?
 
SammyS said:
What is √(2000) ?

What is √(10,000) ?

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:
20√5 and 100, I don't see where you're going with this. Also no calculators are to be used for future reference
Find the largest integer whose square is less than 2000 .

402 = 1600 .

502 = 2500 .

Look at 442 & 452 .
 
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.
 
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?

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

RGV
 
Ray Vickson said:
If an integer does not have an integer square root, does it have a rational square root?

RGV

No

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.

That's the whole question I have been given

SammyS said:
Find the largest integer whose square is less than 2000 .

402 = 1600 .

502 = 2500 .

Look at 442 & 452 .
oh I see, so I how would I go about finding the percentage?
 
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?
How many perfect square integers are there from 1 to 2000 ?

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

How many integers are there from 1 to 2000 ?

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%?

These are not the answers to the questions that Sammy asked.
 
Mark44 said:
These are not the answers to the questions that Sammy asked.
Thanks Mark.

I was also disappointed with OP's response, even though he/she did finally solve the given problem.
 
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.

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.
 
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.