show an example of a rational number that is between √100 and √11
10/3
3.4
3.1
16/5
3.1
To find a rational number that is between √100 and √11, we need to evaluate the decimal equivalents of these square roots.
√100 = 10
√11 ≈ 3.3166
Now, let's examine the given options:
- 10/3 ≈ 3.3333
- 3.4 is slightly larger than √11
- 3.1 is smaller than √11
- 16/5 = 3.2
Based on these options, the rational number that lies between √100 and √11 is 16/5 (which is equal to 3.2 when expressed as a decimal).
To find a rational number between √100 and √11, we need to determine rational numbers that fall within this range.
First, let's compute the values of √100 and √11:
√100 = 10
√11 ≈ 3.316
Now, we can compare the rational numbers in the given options to find one that is between 10 and 3.316:
Option 1: 10/3 ≈ 3.333
Since 3.333 falls after 3.316, it is not between √100 and √11.
Option 2: 3.4
3.4 falls after 3.316, so it is also not between √100 and √11.
Option 3: 3.1
3.1 is smaller than the lower limit of 3.316, so it is not between √100 and √11.
Option 4: 16/5 = 3.2
Since 3.2 falls between 10 and 3.316, it is a rational number between √100 and √11.
Therefore, the rational number that is between √100 and √11 is 16/5.