Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
3.1
3.1
3.4
3.4
165
Start Fraction 16 over 5 end fraction
103
To find a rational number between √10 and √11, we can use decimals.
Let's consider the decimal representation of the given square roots: √10 ≈ 3.162 and √11 ≈ 3.317.
We can choose any rational number between these two decimal values. For example, we can choose the decimal 3.2, which is between 3.162 and 3.317.
Therefore, a rational number that is between √10 and √11 is 3.2.
To find a rational number between √10 and √11, we need to find a number whose square is between 10 and 11.
1. Start by finding the square of the lower bound: √10 ≈ 3.1623, so (3.1623)^2 ≈ 10.
2. Next, find the square of the upper bound: √11 ≈ 3.3166, so (3.3166)^2 ≈ 11.
3. Now, we need to find a rational number between 10 and 11. By looking at the decimals, we can see that 10.165 and 10.103 are between the squares.
Therefore, the rational number between √10 and √11 is 10.165, or in fraction form, 165/10.