To determine which option is an example of an irrational number, let's evaluate each choice:
a) 19
- 19 is a whole number.
- It can be expressed as a fraction where the denominator is 1 (i.e., [tex]\( \frac{19}{1} \)[/tex]).
- Since it can be written as a fraction of two integers, it is a rational number, not irrational.
b) [tex]\(\sqrt{6}\)[/tex]
- The square root of 6.
- 6 is not a perfect square, so [tex]\(\sqrt{6}\)[/tex] cannot be simplified to a fraction of two integers.
- Therefore, [tex]\(\sqrt{6}\)[/tex] is an irrational number.
c) [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex] is already in the form of a fraction.
- It clearly is a ratio of two integers, where 1 is the numerator and 2 is the denominator.
- Hence, [tex]\(\frac{1}{2}\)[/tex] is a rational number.
d) [tex]\(\sqrt{4}\)[/tex]
- The square root of 4.
- 4 is a perfect square, and its square root is 2.
- 2 can be expressed as a fraction (i.e., [tex]\( \frac{2}{1} \)[/tex]).
- Therefore, [tex]\(\sqrt{4} = 2\)[/tex] is a rational number.
After evaluating all the choices, the only number that is an example of an irrational number is:
b) [tex]\(\sqrt{6}\)[/tex]
