The geometric mean of squares of two positive integers is 10. The smallest possible sum of these two integers is

Correct option is A

Given:
The geometric mean of the squares of two positive integers is 10.
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Formula Used:
Geometric Mean of two numbers

​$$\text{Geometric Mean} = \sqrt{x \cdot y} \\$$

Solution:

Let the two positive integers be a and b. Then their squares are 

​$$a^2 \text{ and } b^2. \\\text{So,} \\\sqrt{a^2 \cdot b^2} = \sqrt{(ab)^2} = |ab| \\\sqrt{a^2 \cdot b^2} = 10 \Rightarrow |ab| = 10 \Rightarrow ab = 10 \\$$

Valid pairs:

(1, 10) → Sum = 11

(2, 5) → Sum = 7

(5, 2) → Sum = 7

(10, 1) → Sum = 11

So, the smallest possible sum of the two integers is: 7

Final Answer: (A) 7​​