How many irrational numbers are there between 11−−√ and 17−−√?(1 point)
Responses
four numbers
twenty-eight numbers
an infinite number
six numbers
To determine the number of irrational numbers between 11−−√ and 17−−√, we need to consider that irrational numbers are infinite and non-repeating, so there are an infinite number of them between any two given numbers. Therefore, the correct response is:
an infinite number
To determine the number of irrational numbers between √11 and √17, we can first identify the rational numbers between these two given values and then subtract the total number of rational numbers from the total number of real numbers.
Step 1: Find the rational numbers between √11 and √17.
We know that the square root of a number may be either rational or irrational. Therefore, we need to find the values between √11 and √17 that are rational numbers.
To do this, we can take the square of each number between the two given values and check if the result is a perfect square (meaning it is a rational number). We can perform this calculation:
√11 ≈ 3.31662
√17 ≈ 4.12311
Let's square each value to determine if it is a perfect square:
3.31662^2 ≈ 11
4.12311^2 ≈ 17
Based on this, we can conclude that there are no rational numbers between √11 and √17.
Step 2: Calculate the total number of real numbers between √11 and √17.
Since there are no rational numbers between √11 and √17, all the numbers in this range will be irrational. Therefore, the total number of irrational numbers between √11 and √17 is infinite.
So, the correct answer is "an infinite number" (option C).
The answer is that there are an infinite number of irrational numbers between 11−−√ and 17−−√.
show an example of a rational number that is between 10 and 11?
A. 3.4
B. 16/5
c. 3.1
d. 10/3