The mean propositional of 8a² and $$\frac{18}{a^4}$$​' where a is positive number, is ____________.

Correct option is D

Given:
- First quantity: $$x = 8a^2$$
- Second quantity:  $$y = \frac{18}{a^4}$$
 Formula Used:
The mean proportional M  between two quantities x  and  y  is given by:
$$M = \sqrt{x \cdot y}$$​
Solution:

1. Calculate the product of the two quantities:

$$x \cdot y = 8a^2 \times \frac{18}{a^4} = \frac{8 \times 18 \times a^2}{a^4} = \frac{144a^2}{a^4}$$​

2. Simplify the expression:

$$\frac{144a^2}{a^4} = 144a^{2-4} = 144a^{-2}$$​

3. Take the square root to find the mean proportional:

$$M = \sqrt{144a^{-2}} = \sqrt{144} \times \sqrt{a^{-2}} = 12 \times a^{-1} = \frac{12}{a}$$​

Ans: $$\frac{12}{a}$$​
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