Question

How to find irrational numbers between any two irrational or a rational number

Answer 1

Let us consider an example
√2 and √3 are irrational numbers
√2 = 1.4142 (nearly)
√3 = 1.7321 (nealry)
Now we have to find an irrational number which should lie between 1.4142 and 1.7321
The irrational number is 1.505

In the case of rational number , following steps are needed :

1. Square numerators and denominators of the fractions.
2. Find LCD (Lowest Common Denominator) for denominators and convert all fractions to this LCD.
3. The numerators of the fractions are now perfect squares. Write a new fraction with a numerator that is not a perfect square and between the original fractions' numerators.
4. Put the new fraction inside a square root. The new fraction (inside a square root sign) is now a surd, and an irrational number (also an irrational fraction).