How many irrational numbers are there between 11−−√ and 17−−√?
six numbers
six numbers
an infinite number
an infinite number
four numbers
four numbers
twenty-eight numbers
An irrational number is any real number that is not rational, meaning it cannot be expressed as a fraction of two integers.
To determine the number of irrational numbers between 11−−√ and 17−−√, we need to find the number of perfect squares between the integers 11 and 17.
The square of 3 (√9) is 9, and the square of 4 (√16) is 16.
Therefore, there are 2 perfect squares between 11−−√ and 17−−√.
Since there are an infinite number of irrational numbers between any two consecutive perfect squares, the number of irrational numbers between 11−−√ and 17−−√ is infinite.
To determine the number of irrational numbers between √11 and √17, you can consider the irrational numbers between 11 and 17 first.
First, find the integer values of √11 and √17:
√11 ≈ 3.31662479036
√17 ≈ 4.12310562562
Between these two values, there are the following integers: 4, 5.
To find the number of irrational numbers between these integers, subtract 1 from the larger integer and then multiply the result by 2.
(5 - 1) * 2 = 8
Therefore, there are 8 irrational numbers between √11 and √17.