show how to solve Show an example of a rational number that is between 10−−√
and 11−−√
. if the answer is 16/5
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.
To solve this problem, we need to find a rational number that lies between the given radicals.
First, we need to simplify the radicals:
√10 can be approximated to 3.16
√11 can be approximated to 3.32
Now, we can see that the rational number 16/5 is greater than √10 (approximately 3.16) and smaller than √11 (approximately 3.32). Thus, 16/5 is a rational number that lies between √10 and √11.