Introduction:
In mathematics, rational numbers are those that can be expressed as the quotient or fraction of two integers, whereas irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal representations. Given the range of 25 to 27, we can find both a rational and an irrational number within this interval.

Rational Number:
A rational number can be expressed as the quotient of two integers. To find a rational number between 25 and 27, we can take the average of these two numbers.

Calculation:
Average of 25 and 27:
25 + 27 = 52
52 ÷ 2 = 26

Therefore, 26 is a rational number between 25 and 27.

Irrational Number:
An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal representation. To find an irrational number between 25 and 27, we can utilize the concept of square roots.

Calculation:
Let's consider the square root of 26. The square root of 26 is approximately 5.099. Since the square root of 26 is irrational, we have found an irrational number between 25 and 27.

Summary:
- A rational number is one that can be expressed as the quotient or fraction of two integers.
- An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal representation.
- To find a rational number between 25 and 27, we take the average, which gives us 26.
- To find an irrational number between 25 and 27, we consider the square root of 26, which is approximately 5.099.

26 and root 26