M L Aggarwal Solutions for Exercise 3: EXERCISE 1.3

Classify the following number as rational or irrational.

$\sqrt{23}$

The following real number have decimal expansion of $37.09158$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

The following real number have decimal expansion of $423.\overline{04567}$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

The following real number have decimal expansion of $2.3476817681...$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

The following real number have decimal expansion of $8.9010010001....$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

Find two rational numbers between $2\sqrt{3} \text{and} \sqrt{15}$.

Insert an irrational numbers between $\sqrt{5} \text{and} \sqrt{7}$.

Insert two irrational numbers between $\sqrt{3} \text{and} \sqrt{7}$.