Question

Find two rational number between $\sqrt{2}$ and $\sqrt{3}$.

Answer 1

Since,

$\sqrt{2}=1.414$ (Approximately)

$\sqrt{3}=1.732$ (Approximately)

So, a rational number between those two would be $1.5=\frac{3}{2}$

• But there are several more,
• in fact, infinite number of rational numbers between $\sqrt{2}$ and $\sqrt{3}$.
• Same goes for the number of irrational numbers between any two irrational numbers.

A rational number is made by a ratio $\frac{a}{b}$, where $a,b$ integers, $b\ne 0$

Here are just a few rational numbers, lie between $\sqrt{2}$ and $\sqrt{3}$

$\frac{8}{5}=1.6$

$\frac{5}{3}=\mathrm{1.666666666...}$

$\frac{17}{10}=1.7$

$\frac{29}{20}=1.45$

$\frac{31}{20}=1.55$

$\frac{57}{40}=1.425$

$\frac{69}{40}=1.725$

$\frac{129}{60}=1.6125$