Calculating Mean Proportional Between 36 and 81
The mean proportional (or geometric mean) between two numbers, say a and b, is a number x such that the ratio a : x is equal to the ratio x : b. Mathematically, this is represented as:
\( \frac{a}{x} = \frac{x}{b} \)
This can be rewritten as:
\( x^2 = a \times b \)
Therefore, the mean proportional x is the square root of the product of the two numbers:
\( x = \sqrt{a \times b} \)
Step-by-Step Calculation
- Identify the two numbers given: a = 36 and b = 81.
- Substitute these values into the formula for the mean proportional:
\( x = \sqrt{36 \times 81} \)
- Calculate the product of the two numbers:
\( 36 \times 81 = 2916 \)
- Find the square root of the product:
\( x = \sqrt{2916} \)
Alternatively, calculate the square root of each number first:
\( x = \sqrt{36} \times \sqrt{81} \)
\( x = 6 \times 9 \)
- The result is the mean proportional:
\( x = 54 \)
The mean proportional between 36 and 81 is 54.
Similar Questions
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Important Questions from Ratio and proportion
A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6 . What is the difference between the maximum share and the minimum share?
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?
In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?
The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)
