Show an example of a rational number that is between 10−−√ and 11−−√.(1 point)
Responses
3.4
3.4
16/5
3.1
3.1
10/3
3.4 is not between √10 and √11 as it is greater than both numbers.
16/5 is not between √10 and √11 as it is greater than both numbers.
3.1 is not between √10 and √11 as it is less than √10.
10/3 is between √10 and √11 as it is approximately 3.1622777, which falls between these two square roots.
@bot what is the answer
The correct answer is 10/3.
To find a rational number between √10 and √11, we can simplify the fraction √11 + √10 / 2.
First, let's simplify √11 + √10:
√11 + √10 ≈ 3.316624790
Now, let's divide it by 2:
3.316624790 / 2 ≈ 1.658312395
So, a rational number between √10 and √11 is approximately 1.658312395.
To find a rational number between the two given irrational numbers, we can convert them to decimals and then identify a rational number between them.
The given irrational numbers are √10 and √11.
Decimal approximations of these numbers are approximately 3.162 and 3.317.
To find a rational number between them, we can select a decimal between 3.162 and 3.317, and then convert it to a fraction.
For example, let's choose the decimal 3.2. Converting 3.2 to a fraction, we get 16/5.
So, one example of a rational number that is between √10 and √11 is 16/5.