Question

Find three different irrational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.

Answer 1

Estimate the required three numbers:

The given range of rational numbers are $\frac{2}{3}$ and $\frac{3}{4}$.

Multiplying the first number by $16$ and the second number by $12$ on both numerator and denominator we get,

$\frac{32}{48}$ and $\frac{36}{48}$

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

$\frac{33}{48},\frac{34}{48}$ and $\frac{35}{48}$

Hence, the three different irrational numbers between $\frac{2}{3}$ and $\frac{3}{4}$are $\frac{33}{48},\frac{34}{48}$ and $\frac{35}{48}$.