Answer:
The rational numbers are [tex]\frac{11}{3}, 6.25, 0.01045,\sqrt{\frac{16}{81}},0.\bar{42}[/tex] and the irrational functions are [tex]\sqrt{48},\sqrt{\frac{3}{16}}[/tex].
Step-by-step explanation:
A rational number can be expressed in the form of [tex]\frac{p}{q}[/tex], where p and q are integers and q is not equal to 0. For example [tex]2,3.5,\frac{2}{5},...[/tex].
An irrational function can not be expressed in the form of [tex]\frac{p}{q}[/tex], where p and q are integers and q is not equal to 0. For example [tex]\sqrt{2},\sqrt{3},\sqrt{5},...[/tex].
If any number is multiplied by a irrational number then the resultant number is an irrational number.
By the above definition we can conclude that:
The number [tex]\frac{11}{3}[/tex] is a rational number.
[tex]\sqrt{48}=\sqrt{16\times 3}=4\sqrt{3}[/tex]
Therefore [tex]\sqrt{48}[/tex] is an irrational number.
[tex]6.25=\frac{625}{100}=\frac{25}{4}[/tex]
Therefore 6.25 is a rational number.
[tex]0.01045=\frac{1045}{100000}=\frac{209}{20000}[/tex]
Therefore 0.01045 is a rational number.
[tex]\sqrt{\frac{16}{81}}=\frac{4}{9}[/tex]
The number [tex]\frac{16}{81}[/tex] is a rational number.
[tex]\sqrt{\frac{3}{16}}=\frac{\sqrt{3}}{4}[/tex]
The number [tex]\frac{3}{14}[/tex] is an irrational number.
[tex]0.\bar{42}=\frac{42}{99}[/tex]
Therefore [tex]0.\bar{42}[/tex] is an irrational number. The numbers with recursive bar are always rational numbers.
