# Percentage of √n

1. Jul 29, 2012

### phospho

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.

2. Jul 29, 2012

### SammyS

Staff Emeritus

What is √(2000) ?

What is √(10,000) ?

3. Jul 29, 2012

### phospho

20√5 and 100, I don't see where you're going with this. Also no calculators are to be used for future reference

4. Jul 29, 2012

### SammyS

Staff Emeritus
Find the largest integer whose square is less than 2000 .

402 = 1600 .

502 = 2500 .

Look at 442 & 452 .

5. Jul 29, 2012

### HallsofIvy

Staff Emeritus
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.

6. Jul 29, 2012

### Ray Vickson

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

RGV

7. Jul 29, 2012

### phospho

No

That's the whole question I have been given

oh I see, so I how would I go about finding the percentage?

8. Jul 29, 2012

### SammyS

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

How many integers are there from 1 to 2000 ?

9. Jul 30, 2012

### phospho

So 2.2 and 1%?

10. Jul 30, 2012

### Mentallic

Yep.

11. Jul 30, 2012

### Staff: Mentor

12. Jul 30, 2012

### SammyS

Staff Emeritus
Thanks Mark.

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

13. Jul 30, 2012

### phospho

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.

14. Jul 30, 2012

### Staff: Mentor

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.