Show an example of an irrational number between 9 and 11.
A. √99
B. √10
C. √100
D. √20
B. √10
9^2 = 81
11^2 = 121
so it has to be between sqrt 81 and sqrt 121
the only ones are sqrt 99 and sqrt 100
sqrt 100 is no good because 10 is rational (20/2 for example)
so I think sqrt 99
A
Yes, you are correct. √99 is an example of an irrational number between 9 and 11.
To determine if any of the given options are irrational numbers, we need to recall the definition of an irrational number. An irrational number is a real number that cannot be written as a simple fraction or a terminating or repeating decimal.
Now, let's evaluate each of the options:
A. √99: To determine if this is an irrational number, we need to find its decimal representation. The square root of 99 is approximately equal to 9.949874371. Since this decimal neither terminates nor repeats, it is an irrational number.
B. √10: Similarly, we need to find the decimal representation of √10. The square root of 10 is approximately equal to 3.16227766. Once again, this decimal neither terminates nor repeats, so it is an irrational number.
C. √100: The square root of 100 is equal to 10. This is not an irrational number because it can be written as the fraction 10/1, which is a rational number.
D. √20: Finally, we need to find the decimal representation of √20. The square root of 20 is approximately equal to 4.472135955. Since this decimal neither terminates nor repeats, it is an irrational number.
Therefore, an example of an irrational number between 9 and 11 is option B: √10.