The Mean Proportional (also called Geometric Mean) is a concept in ratio and proportion used in Class 9 and 10 Mathematics.
Mean proportional is different from arithmetic mean. AM of 4 and 16 = 10, but mean proportional = 8.
If a and b are two numbers, their Mean Proportional x satisfies:
a : x = x : b
This gives: x² = a × b
Therefore: x = √(a × b)
Example 1: Find the mean proportional of 4 and 16. x = √(4 × 16) = √64 = 8
Verification: 4 : 8 = 8 : 16 ✓ (both equal 1:2)
Example 2: Find the mean proportional of 9 and 25. x = √(9 × 25) = √225 = 15
x = √(3 × 27) = √81 = **9**
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