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The mean proportional between 0.06 and 24 is:
0.012
12
0.12
2
2
Multiply the numbers first: 0.06├Ч24=1.44. Then take the square root of 1.44, which is 1.2.
Two numbers a = 0.06 and b = 24
x=a├ЧbтАЛ
Multiply the numbers first: 0.06├Ч24=1.44. Then take the square root of 1.44, which is 1.2.
Many students mistake 0.06 for 0.6 or multiply incorrectly, leading to 0.12 or 12, whereas 1.44тАЛ is 1.2.
Define the mean proportional
The mean proportional x between two numbers a and b is given by the geometric mean formula, where a/x=x/b.
x=a├ЧbтАЛ
Substitute the values
Plug a=0.06 and b=24 into the formula.
x=0.06├Ч24тАЛ
Calculate the product
Multiply 0.06 by 24 to get 1.44.
0.06├Ч24=1.44
Find the square root
Calculate the square root of 1.44 to determine the mean proportional.
x=1.44тАЛ=1.2
D is correct because the square root of (0.06 ├Ч 24) is 1.2.
This concept is a foundation for solving problems in Ratio and Proportion and is frequently used in calculating segments in geometry (e.g., altitude in a right-angled triangle).
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