Question

Find three different irrational numbers between $\frac{5}{7}$ and $\frac{9}{11}$.

Answer 1

Estimate the required three numbers:

The given range of rational numbers are $\frac{5}{7}$ and $\frac{9}{11}$.

Multiplying the first number by $11$ and the second number by $7$ on both numerator and denominator we get,

$\frac{55}{77}$ and $\frac{63}{77}$

Since the denominator is the same, the three irrational numbers between them are,

$\frac{56}{77},\frac{57}{77}$ and $\frac{58}{77}$

Hence, the three different irrational numbers between $\frac{5}{7}$ and $\frac{9}{11}$are $\frac{56}{77},\frac{57}{77}$ and $\frac{58}{77}$.