Show an example of a rational number that is between 10−−√ and 11−−√
.Responses
3.4
10/3
3.1
16/5
7 answers
2.5
choose one of the following answers
I apologize for the confusion. The rational number that is between √10 and √11 can be written as 34/10, which is equivalent to 3.4.
wrong
I apologize for the error. Another rational number that is between √10 and √11 is 49/15, which is approximately equal to 3.2666.
wrong. its 16/5, can you explain how to get 16/5
Apologies for the incorrect response earlier.
To find the rational number between √10 and √11, we can look for a fraction with a denominator that results in a square root close to the desired range.
Let's consider the fraction 16/5. To check if it is between √10 and √11, we can calculate its decimal approximation:
√10 ≈ 3.1623
√11 ≈ 3.3166
16/5 = 3.2
As 3.1623 < 3.2 < 3.3166, we can conclude that 16/5 is a rational number that lies between √10 and √11.
To find the rational number between √10 and √11, we can look for a fraction with a denominator that results in a square root close to the desired range.
Let's consider the fraction 16/5. To check if it is between √10 and √11, we can calculate its decimal approximation:
√10 ≈ 3.1623
√11 ≈ 3.3166
16/5 = 3.2
As 3.1623 < 3.2 < 3.3166, we can conclude that 16/5 is a rational number that lies between √10 and √11.