Find three rational and irrational number …

Since we know that rational number between two rational numbers is obtained by {tex}\frac{1}{2}{/tex}[a+b]
A rational number lying between -2 and -3 is {tex}\frac{1}{2}{/tex}[(-2) + (-3)],
i.e.,{tex}-\frac{5}{2}{/tex}
Now, a rational number lying between -2 and{tex}-\frac{5}{2}{/tex}is
{tex}\left.\frac{1}{2}[(-2)+\left(-\frac{5}{2}\right)\right ]{/tex}
= {tex} \frac{1}{2} \times\left(-\frac{9}{2}\right) {/tex}
= {tex}-\frac{9}{4} {/tex}
And, a rational number lying between {tex}-\frac{5}{2}{/tex} and -3 is
{tex}\frac{1}{2}\left(\left(-\frac{5}{2}\right)+(-3)\right) {/tex}
{tex}\frac{1}{2} \times\left(-\frac{11}{2}\right){/tex}
{tex}-\frac{11}{4} {/tex}
Thus, we have {tex}-2>-\frac{9}{4}>-\frac{5}{2}>-\frac{11}{4}>3{/tex}
Hence, three rational numbers between -2 and -3 are {tex}-\frac{9}{4},-\frac{5}{2}{/tex} and {tex}-\frac{11}{4}{/tex}