Mean Proportional
The mean proportional is a term used in mathematics to refer to the middle number between two numbers in a proportion. It is also known as the geometric mean. In other words, the mean proportional between two numbers 'a' and 'b' is the square root of their product, i.e., sqrt(a*b).

Calculating Mean Proportional between 25,81
To find the mean proportional between 25 and 81, we can use the formula mentioned above, which is sqrt(a*b).

So, the mean proportional between 25 and 81 is:
sqrt(25*81) = sqrt(2025) = 45

Hence, the mean proportional between 25 and 81 is 45.

Explanation
In this question, we are asked to find the mean proportional between 25 and 81. To do so, we first need to understand what mean proportional means. As mentioned earlier, the mean proportional is the middle number between two numbers in a proportion, and it can be found by taking the square root of their product.

In this case, we have two numbers, 25 and 81. To find the mean proportional between these two numbers, we first need to multiply them, which gives us 2025. Then, we take the square root of 2025, which is 45. Therefore, 45 is the mean proportional between 25 and 81.

Conclusion
The mean proportional between 25 and 81 is 45. The formula to find the mean proportional is sqrt(a*b), where 'a' and 'b' are the two numbers in the proportion. By multiplying the two numbers and taking the square root of the product, we can find the mean proportional.

25 : x :: x : 81
x=√25×81
x=45