Question

find a rational and irrational number between two positive numbers a and b

Answer 1

Given:

Consider the two positive given numbers a and b

Find:

We need to calculate a rational and irrational number between a and b

Solution:

We know that the average of the two number is rational number between them.

Also the square root of product of two two numbers are irrational number between them.

Therefore

Rational between a and b = $\frac{a+b}{2}$

Irrational between a and b = $\sqrt{ab}$