How many irrational numbers are there between 11−−√
and 17−−√
(1 point)
Responses
six numbers
six numbers
twenty-eight numbers
twenty-eight numbers
four numbers
four numbers
an infinite number
an infinite number
There is an infinite number of irrational numbers between √11 and √17.
exsplin
To determine the number of irrational numbers between 11−−√ and 17−−√, we need to find the irrational numbers within this range. Since irrational numbers are non-repeating and non-terminating decimals, there are an infinite number of irrational numbers between any two given values. Therefore, the correct answer is: an infinite number.
To determine the number of irrational numbers between √11 and √17, we need to understand what irrational numbers are. Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They include numbers like π (pi) and √2 (square root of 2).
In this case, we are looking for all the irrational numbers between √11 and √17. To find them, we can start by approximating the square roots to get an idea of the range.
√11 is approximately 3.316 and √17 is approximately 4.123.
Now, let's think about the irrational numbers that lie between these approximations. We can see that there are several irrational numbers in this range, such as √2 and √3.
To find the exact number, we need to consider that between any two irrational numbers, there are infinitely many other irrational numbers. This is because irrational numbers are dense in the real number line.
Therefore, the correct answer is that there are an infinite number of irrational numbers between √11 and √17.