Rational Numbers between √2 and √3:
- 2.1: This number lies between √2 (approximately 1.41) and √3 (approximately 1.73) and is a rational number as it can be expressed as 21/10.
- 2.2: Another rational number between √2 and √3 is 2.2, which is equivalent to 11/5.
- 2.5: 2.5 is also a rational number between √2 and √3 as it can be expressed as 5/2.
- 2.7: Similarly, 2.7 falls between √2 and √3 and can be represented as 27/10.
- 2.9: Lastly, 2.9 is a rational number between √2 and √3 and can be written as 29/10.

Irrational Numbers between √2 and √3:
- √2.1: This number is irrational as it is the square root of an irrational number (4.41).
- √2.3: Similarly, √2.3 is an irrational number as it is the square root of 5.29, which is irrational.
- √2.4: √2.4 is also irrational as it is the square root of an irrational number (5.76).
- √2.5: Another irrational number between √2 and √3 is √2.5, which is the square root of 6.25.
- √2.8: Lastly, √2.8 is an irrational number as it is the square root of 7.84, which is irrational.
By understanding the nature of rational and irrational numbers, we can identify specific numbers that fall between √2 and √3. Rational numbers can be expressed as fractions, while irrational numbers cannot be represented as fractions and have non-repeating, non-terminating decimal expansions.