Mean Proportional between 12x^2 and 27y^2

To find the mean proportional between two numbers, we need to find a number that is equal to the square root of the product of the two given numbers. In this case, we are looking for the mean proportional between 12x^2 and 27y^2.

Step 1: Find the product of the two given numbers
The product of 12x^2 and 27y^2 can be calculated by multiplying the numerical coefficients and the variables separately.

12x^2 * 27y^2 = 12 * 27 * x^2 * y^2 = 324 * x^2 * y^2

Step 2: Take the square root of the product
To find the mean proportional, we need to take the square root of the product obtained in the previous step.

√(324 * x^2 * y^2) = √324 * √(x^2 * y^2) = 18 * xy

Therefore, the mean proportional between 12x^2 and 27y^2 is 18xy.

Explanation:
The mean proportional between two numbers is a value that lies between the given numbers and satisfies the condition that the product of the mean proportional and the second number is equal to the product of the first and second numbers. In this case, the mean proportional between 12x^2 and 27y^2 is 18xy.

Summary:
To find the mean proportional between 12x^2 and 27y^2, we first calculate the product of the two numbers. Then, we take the square root of the product to obtain the mean proportional. In this case, the mean proportional is 18xy.