Explanation
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero
[tex]\begin{gathered} a=\frac{p}{q} \\ q\ne0 \\ a\text{ is rational } \end{gathered}[/tex]and An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio
so,let's check every option
Step 1
a)-13/3
it is a fraction, so it is a rational number
b)
[tex]\begin{gathered} 0.1234 \\ 0.1234*\frac{10000}{10000}=\frac{1234}{1000} \\ so,\text{ the number can be expressed as a ratio, hence} \end{gathered}[/tex]it is a rational number
c)
[tex]\sqrt{37}=6.0827625302...[/tex]Square root of 37 is an irrational number, because the value of √37 is a non-teminating decimal
d)-77
The rational numbers include all the integers, and this is a integer, so this is a rational number
d)
[tex]\begin{gathered} -\sqrt{100} \\ -\sqrt{100}=\text{ -10} \end{gathered}[/tex]The rational numbers include all the integers, and this is a integer, so this is a rational number
e)
[tex]\begin{gathered} -\sqrt{12} \\ -\sqrt{12}=-\sqrt{4*3} \\ -12=-\sqrt{4\times3}\text{ = -}\sqrt{4}\sqrt{3\text{ }}=\text{ -2}\sqrt{3} \end{gathered}[/tex]The sqrt of 3 is irrational. Specifically, it cannot be written as the ratio of two given numbers or be written as a simple fraction,so
this number is a irrational number
I hope this helps you