we know that
Rational Number is a number that can be made by dividing two integers, and an Irrational Number is a real number that cannot be written as a simple fraction
so
case a) [tex]\sqrt{3} +6[/tex]
[tex]\sqrt{3} +6=7.732050807...[/tex] ------> is an irrational number
case b) [tex]\sqrt{36} -\pi[/tex]
[tex]\sqrt{36} -\pi=6-\pi=2.858407...[/tex] ------> is an irrational number
case c) [tex]\sqrt{144} *0.25[/tex]
[tex]\sqrt{144} *0.25=12*0.25=3[/tex]
we know that
All whole numbers are rational numbers.
therefore
the case c) is a rational number
case d) [tex]\frac{\sqrt{4}}{\sqrt{2}}[/tex]
[tex]\frac{\sqrt{4}}{\sqrt{2}}=\sqrt{2}=1.41421356..[/tex] ------> is an irrational number
therefore
the answer is
[tex]\sqrt{144} *0.25[/tex] is a rational number
