The square root of 0.15 × 0.35 × 0.21 is :

Appeared in: NHM UP Staff Nurse - 2019

Explanation

The problem requires finding the square root of the product of three decimal numbers: 0.15, 0.35, and 0.21.
First, multiply the numbers: 0.15 × 0.35 × 0.21 = 0.011025.
Next, find the square root of the product: √0.011025.
This can be simplified by converting to a fraction: √(11025 / 1000000) = √11025 / √1000000 = 105 / 1000.
The final result is 105 divided by 1000, which equals 0.105.

Option A: This value is incorrect. It might result from a miscalculation, possibly by misplacing the decimal point after finding the product of the numerators (3 × 5 × 7 = 105) and then dividing by 10,000 instead of 1,000.
Option C: This is the result of finding the square root of the numerator (√11025 = 105) but failing to divide by the square root of the denominator (√1000000 = 1000).
Option D: This value is incorrect and likely arises from a decimal placement error, possibly by dividing 105 by 100 instead of 1000.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the square root of a product of decimal numbers as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, numerical proficiency is crucial in nursing for tasks like medication dosage calculations, IV drip rate adjustments, and interpreting lab results.
A misplaced decimal point in a clinical calculation can lead to significant medication errors, potentially causing serious harm to a patient. This question reinforces the importance of precision.
What if the numbers were 1.5, 3.5, and 2.1? The product would be 11.025, and its square root would be approximately 3.32, demonstrating how a shift in the decimal point dramatically changes the outcome.

How to Approach the Question

First, carefully read the question to understand the mathematical operation required, which is finding the square root of a product.
Multiply the given decimal numbers: 0.15 × 0.35 × 0.21.
The product is 0.011025.
Now, calculate the square root of 0.011025. A helpful trick is to convert the decimal to a fraction (11025/1000000).
Find the square root of the numerator (105) and the denominator (1000) separately.
Divide the results (105/1000) to get the final answer, 0.105, and match it with the given options.

Concept Tested & Keywords

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Practise the full NHM UP Staff Nurse - 2019

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