Show an example of an irrational number between 9 and 11
A. √10
B. √99
C. √20
D. √100
B. √99
√99 is an irrational number between 9 and 11, because it cannot be expressed as a fraction and its decimal representation goes on forever without repeating.
To find an irrational number, we need to check if the square root of a number is not a whole number or a fraction. Let's check each option:
A. √10: Taking the square root of 10 results in approximately 3.1622776601683795, which is not a whole number or fraction. Therefore, it is an irrational number.
B. √99: The square root of 99 is approximately 9.9498743710662, which is not a whole number or fraction. Hence, it is an irrational number.
C. √20: The square root of 20 is approximately 4.47213595499958, which is not a whole number or fraction. It is also an irrational number.
D. √100: Taking the square root of 100 gives us a whole number, 10. Therefore, it is not an irrational number.
Therefore, the irrational number between 9 and 11 is option A, √10.