We know root2= 1.414.... and root3= 1.736..... rational between root2 and root3 can be 1.42 and an irrational number can be 1.707007000.....

Understanding Rational and Irrational Numbers
Rational numbers are those that can be expressed as the quotient of two integers, while irrational numbers cannot be expressed as such. Between the square roots of 2 (√2) and 3 (√3), we can find both rational and irrational numbers.
Finding a Rational Number Between √2 and √3
1. Approximate Values:
- √2 is approximately 1.414.
- √3 is approximately 1.732.
2. Choosing a Rational Number:
- A simple rational number between these two values is 1.5 (or 3/2).
- This number is rational because it can be expressed as the ratio of two integers (3 and 2).
Verifying the Choice
- Comparison:
- 1.5 is greater than √2 (1.414) and less than √3 (1.732).
- Therefore, it fits perfectly between the two.
Conclusion
- You can find many rational numbers between √2 and √3. For instance, numbers like 1.6 (8/5), 1.7 (17/10), or even fractions like 5/4 also lie within this range.
- The density of rational numbers ensures that there are infinitely many options in any interval between two irrational numbers.
Finding rational numbers between irrational numbers provides a practical way to understand the number line and the relationship between different types of numbers.