Question

Find an irrational number between $\frac{5}{7}$ and $\frac{7}{9}$. How many more there may be?

Answer 1

$\frac{5}{7}$ and $\frac{7}{9}$ are two rational numbers.

To find, an irrational number between $\frac{5}{7}$ and $\frac{7}{9}$.

Square root of given number $\frac{5}{7}$ multiplied by square root of $\frac{7}{9}$ we get,

an irrational number $=$$\frac{\sqrt{5}\times \sqrt{7}}{\sqrt{7}\times \sqrt{9}}$$=\sqrt{\frac{5}{9}}=\frac{\sqrt{5}}{3}$.

Then, the irrational number is $\frac{\sqrt{5}}{3}$.

And we get infinite number of irrational numbers between two rational numbers.