Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
165
Start Fraction 16 over 5 end fraction
3.1
3.1
103
Start Fraction 10 over 3 end fraction
3.4
Start Fraction 3 over 1 end fraction
To find a rational number between √10 and √11, we need to express these square roots as decimals.
First, let's calculate the decimal value of √10 and √11 using a calculator:
√10 ≈ 3.16227766017
√11 ≈ 3.31662479036
Now, we can find a rational number between these two decimal values. One way to do this is by taking the average of the two decimals:
(3.16227766017 + 3.31662479036) / 2 ≈ 3.23945122527
Therefore, 3.23945122527 is a rational number between √10 and √11.