4. which numbers are irrational? 11, $sqrt{15}$, - 14, $\frac{5}{7}$, $\frac{9}{4}$, 0.151155111555...

Explanation:

Step1: Recall definition of rational numbers

Rational numbers can be written as $\frac{p}{q}$ where $p,q$ are integers and $q\neq0$. Integers are rational. So 11 and - 14 are rational as they can be written as $\frac{11}{1}$ and $\frac{-14}{1}$ respectively. $\frac{5}{7}$ and $\frac{9}{4}$ are in $\frac{p}{q}$ form, so they are rational.

Step2: Recall definition of irrational numbers

Irrational numbers cannot be written as a fraction $\frac{p}{q}$. $\sqrt{15}$ is irrational because 15 is not a perfect - square and its decimal expansion is non - repeating and non - terminating. The number 0.151155111555... is non - repeating and non - terminating, so it is also irrational.

Answer:

$\sqrt{15},0.151155111555...$