- OSSSC Nursing Officer-2021

OSSSC Nursing Officer-2021

Quantitative Aptitude and Mathematics

Hard

Appeared in: OSSSC Nursing Officer-2021

Explanation

The core of this problem is simplifying each radical by factoring out the largest perfect square from the number under the root.
After factoring, the terms become: √24 = 2√6, √216 = 6√6, and √96 = 4√6.
Substituting these into the expression gives (2√6 + 6√6) / 4√6.
The numerator simplifies to 8√6 by adding the coefficients of the like radicals.
The expression becomes 8√6 / 4√6. The √6 terms cancel out, leaving 8/4.
The final simplification of 8 divided by 4 yields the answer 2.

Option A: This is the simplified form of only the first term in the numerator, √24. This error occurs if the student simplifies only one part of the expression and ignores the rest of the calculation.
Option B: This value does not arise from a straightforward simplification of the expression. It may result from incorrect factoring of the numbers under the radicals or other calculation mistakes.
Option D: This answer may result from multiple errors, such as incorrectly handling the fraction after simplification. For example, if one were to simplify 2√6 / 4√6, the answer would be 1/2, but the √6 term should not be present.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of expressions involving square roots (radicals) as background academic context rather than a clinical decision trigger.
While this specific problem is abstract, proficiency in basic mathematics is a foundational skill for nurses.
Accurate calculation is critical in clinical practice for tasks like medication dosage calculation, IV drip rate adjustments, and interpreting clinical data, where a small error can have significant patient safety implications.
What if? If the denominator was √24 instead of √96, the expression would be (8√6) / (2√6), and the answer would be 4. This shows how each number in the expression is critical to the final result.

How to Approach the Question

First, analyze the expression to identify the mathematical operations required. This problem involves addition and division of square roots.
The primary strategy is to simplify each radical term individually. To do this, find the largest perfect square that is a factor of the number inside the square root (the radicand).
For example, for √24, the factors are (1, 24), (2, 12), (3, 8), and (4, 6). The largest perfect square factor is 4. So, √24 = √(4 × 6) = 2√6.
Repeat this simplification for all radical terms in the expression.
After simplifying, substitute the new forms back into the original expression.
Combine any 'like terms' (terms with the same radical part) in the numerator or denominator by adding or subtracting their coefficients.

Concept Tested & Keywords

Concept Tested: Simplification of expressions involving square roots (radicals).
Stem keywords: √24, √216, √96, Simplification, Radicals
Lead-in keywords: Solve, Evaluate
Negative lead-in flag: false

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Practise the full OSSSC Nursing Officer-2021

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