Rational √n Percentages: 1 ≤ n ≤ 2000 & 1 ≤ n ≤ 10,000

[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.

No idea how to go about this, any help?

 

[SammyS]

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) ?

 

[phospho]

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

 

[SammyS]

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 .

 

[HallsofIvy]

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.

 

[Ray Vickson]

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

 

[phospho]

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

RGV

No

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

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?

 

[SammyS]

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 ?

 

[phospho]

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%?

 

[Mentallic]

So 2.2 and 1%?

Yep.

 

[Mark44]

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%?

These are not the answers to the questions that Sammy asked.

 

[SammyS]

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.

 

[phospho]

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.

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.

 

[Mark44]

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.