Question

show how to solve Show an example of a rational number that is between 10−−√
and 11−−√
. if the answer is 16/5

Answer 1

To find a rational number between √10 and √11, we can consider expressing both numbers as decimals and then finding a rational number between those two decimal representations.

Let's convert both √10 and √11 to decimals using a calculator:

√10 ≈ 3.16227766017
√11 ≈ 3.31662479036

Now we can see that a rational number between these two decimal values would be approximately 3.2. We can express 3.2 as a fraction:

3.2 = 3 + 0.2 = 3 + 2/10 = 3 + 1/5

Therefore, the rational number that is between √10 and √11 is 16/5.