Find the mean proportional of 32 and 98.

Appeared in: Bihar NHM CHO-2025

Explanation

The mean proportional, also known as the geometric mean, of two numbers 'a' and 'b' is the square root of their product (√(a × b)).
First, multiply the two given numbers: 32 × 98 = 3136.
Next, find the square root of the product: √3136 = 56.
Thus, 56 is the mean proportional of 32 and 98.

Option A: This is incorrect. The square of 53 is 53² = 2809, which is not the product of 32 and 98 (3136).
Option C: This is incorrect. The square of 54 is 54² = 2916, which is not the product of 32 and 98 (3136).
Option D: This is incorrect. The square of 57 is 57² = 3249, which is not the product of 32 and 98 (3136).

Visual 1: No visual is required for this type of mathematical calculation question.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of mean proportional (geometric mean) of two numbers as background academic context rather than a clinical decision trigger.
This is a general mathematics question testing numerical ability and is not directly related to clinical nursing practice.
However, strong numeracy skills are essential for nurses for tasks like medication dosage calculations, IV drip rate monitoring, and interpreting lab results.
What if? If the numbers were 8 and 18, the product would be 8 × 18 = 144, and the mean proportional would be √144 = 12.

How to Approach the Question

First, identify the key terms in the question: 'mean proportional', '32', and '98'.
Recall the definition of mean proportional: for two numbers 'a' and 'b', it is the square root of their product (√(a × b)).
Substitute the given numbers into the formula: a = 32 and b = 98.
Perform the multiplication: 32 × 98 = 3136.
Calculate the square root of the result: √3136 = 56.
Compare your result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculation of mean proportional (geometric mean) of two numbers.
Stem keywords: mean proportional, 32, 98
Lead-in keywords: Find

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Practise the full Bihar NHM CHO-2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.