The mean proportional of $ 25 $ and $ 36 $ is:

Question

Examoogle · Accepted Answer

The correct answer is Option D: 30. The mean proportional of two numbers $a$ and $b$ is simply the geometric mean, which is the square root of their product. Here, $\sqrt{25 	imes 36} = \sqrt{25} 	imes \sqrt{36} = 5 	imes 6 = 30$.

Step-by-Step Solution & Concepts:
Shortcut Trick: The mean proportional of two numbers $a$ and $b$ is simply the geometric mean, which is the square root of their product. Here, $\sqrt{25 	imes 36} = \sqrt{25} 	imes \sqrt{36} = 5 	imes 6 = 30$.

Formula Used: $$x = \sqrt{a 	imes b}$$

Given: Two numbers are 25 and 36.

Steps: Define the formula: The mean proportional $x$ of two numbers $a$ and $b$ is given by the square root of their product.. Substitute the values: Given $a = 25$ and $b = 36$, substitute these into the formula.. Calculate the square root: Calculate the product or separate the square roots: $\sqrt{25} 	imes \sqrt{36} = 5 	imes 6$.

Answer: D is correct because the square root of the product of 25 and 36 is $\sqrt{900}$, which equals 30.

Exam Tip: This concept is foundational for understanding similar triangles and the geometric mean theorem in Euclidean geometry.

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