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Find the mean proportional of 36 and 9.
18
27
12
15
18
Calculate the square root of the product of the two numbers. Since 36=62 and 9=32, the result is 6├Ч3=18.
Two numbers are provided: a = 36 and b = 9.
x=a├ЧbтАЛ
Calculate the square root of the product of the two numbers. Since 36=62 and 9=32, the result is 6├Ч3=18.
Many students mistakenly calculate the arithmetic mean 2a+bтАЛ=22.5 instead of the mean proportional (geometric mean).
Define the formula
The mean proportional x of two numbers a and b is given by the square root of their product.
x=a├ЧbтАЛ
Substitute the values
Given a=36 and b=9, substitute these into the formula.
x=36├Ч9тАЛ
Calculate the result
Multiply the numbers inside the square root to get 324, then find the square root, or take the square root of each factor individually: 36тАЛ├Ч9тАЛ=6├Ч3=18.
x=324тАЛ=18
A is correct because the mean proportional calculation 36├Ч9тАЛ results in 18.
This concept is a special case of the geometric progression where the middle term b in a,b,c satisfies b2=ac. This frequently appears in problems involving geometric series and properties of triangles.
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