Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
3.1
3.4
16/5
10/3
The rational number between √10 and √11 would be 16/5, as it is approximately 3.2 and lies between the values 3.1 and 3.4.
so its 16/3?
To find a rational number between √10 and √11, we can convert both numbers to decimals to make comparisons easier.
√10 is approximately 3.1622 and √11 is approximately 3.3166.
We can see that 3.1 (which is less than 3.1622) is a rational number between √10 and √11.
Therefore, the rational number between 10−−√ and 11−−√ is 3.1.
To find a rational number between √10 and √11, you can start by approximating the square roots to decimal values.
√10 is approximately 3.16, and √11 is approximately 3.32.
Now, you can choose a rational number between these two values. Let's consider the options given:
- 3.1 is between 3.16 and 3.32, so it is a valid option.
- 3.4 is greater than 3.32, so it is not a valid option.
- 16/5 is approximately 3.20, which is between 3.16 and 3.32, so it is a valid option.
- 10/3 is approximately 3.33, which is greater than 3.32, so it is not a valid option.
Thus, the rational numbers that are between √10 and √11 are 3.1 and 16/5.