Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
165
Start Fraction 16 over 5 end fraction
3.4
3.4
3.1
3.1
103
Start Fraction 103 over 10 end fraction (or 10.3)
To find a rational number between √10 and √11, we can use the concept of a decimal representation.
First, let's simplify the square roots:
√10 ≈ 3.1623
√11 ≈ 3.3166
Now, let's find a rational number between these two values. One way to do this is by taking the average of the two square roots:
(3.1623 + 3.3166) ÷ 2 ≈ 3.23945
So, a rational number between √10 and √11 is approximately 3.23945.