What will be the mean proportional value between 6 and 24?

Question

Accepted Answer

The correct option is 4:
To find the mean proportional (also known as the geometric mean) between two numbers, say $a$ and $b$, we use the formula:
$$Mean : Proportional = \sqrt{a \times b}$$
In this question, we need to find the mean proportional between 6 and 24.
Here, $a = 6$ and $b = 24$.
Substitute these values into the formula:
$$Mean : Proportional = \sqrt{6 \times 24}$$
$$Mean : Proportional = \sqrt{144}$$
Now, calculate the square root of 144:
$$Mean : Proportional = 12$$
Therefore, the mean proportional value between 6 and 24 is 12.

The incorrect option is 1: This option (4) is incorrect because it is the square root of 16, not the mean proportional of 6 and 24.
The incorrect option is 2: This option (18) is incorrect because it might be obtained by incorrectly adding or using an arithmetic mean instead of a geometric mean. For example, $(6+24)/2 = 15$, which is also not 18, so this value does not correspond to a common mathematical operation for mean proportional.
The incorrect option is 3: This option (30) is incorrect because it is the sum of the two numbers ($6+24=30$), not the mean proportional.