Question

Find 3 irrational numbers between $\frac{5}{7}$ and $\frac{11}{9}$. Give solution.

Answer 1

First step will be to make the same denominator of both fractions.
So we need to find irrational numbers between $\frac{45}{63}$ and $\frac{77}{63}$
$\frac{45}{63}$ can be written as $\sqrt{\frac{2025}{63}}$
$\frac{77}{63}$ can be written as $\sqrt{\frac{5929}{63}}$
So irrational numbers between $\frac{5}{7}$ and $\frac{11}{9}$ will be $\sqrt{\frac{2026}{63}};\sqrt{\frac{2027}{63}};\sqrt{\frac{2030}{63}}$.