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.
Rational √n percentages are percentages that can be expressed as the square root of a rational number. In other words, the percentage can be written as a fraction with a square root in the numerator and a whole number in the denominator.
The range of n for these percentages is between 1 and 2000 for the first set of numbers and between 1 and 10,000 for the second set. This means that the square root of any number within these ranges can be expressed as a rational percentage.
These percentages are important because they can be used to represent fractions in a more visually intuitive way. They can also be helpful in certain calculations and can provide a better understanding of the relationship between fractions and percentages.
To calculate a rational √n percentage, you simply take the square root of the chosen number and express it as a fraction. For example, if n = 25, the rational √n percentage would be √25/1 or 5/1, which is equivalent to 500%.
No, irrational numbers cannot be expressed as rational √n percentages because they cannot be written as a fraction with a square root in the numerator and a whole number in the denominator. Only numbers that can be expressed as a ratio of two integers can be written as rational √n percentages.