- ESIC Nursing Officer 2016 (Shift -2)

ESIC Nursing Officer 2016 (Shift -2)

Non Nursing Subjects

Hard

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The core task is to simplify the expression 3√2 + √18 - (1/2)√8.
The terms √18 and √8 must be simplified first. √18 simplifies to 3√2, and (1/2)√8 simplifies to √2.
Substituting these back gives 3√2 + 3√2 - √2.
Combining the coefficients (3 + 3 - 1) results in 5, making the final answer 5√2.

Option B: This result (6√2) is obtained if the last term (√2) is ignored or incorrectly added, i.e., 3√2 + 3√2 = 6√2.
Option C: This result (4√2) would stem from a miscalculation when combining the coefficients, for example, incorrectly calculating 3 + 3 - 1.
Option D: This result (7√2) is obtained if the last term is incorrectly added instead of subtracted: 3√2 + 3√2 + √2 = 7√2.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process of simplifying the radical expression. It would show breaking down √18 and √8, substituting them back, and combining the like terms to reach the final answer.

Clinical Relevance

Nursing practice connection: Knowing Simplification of expressions involving radicals (square roots) helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
This is a general mathematics question testing algebraic skills, not a nursing-specific concept.
While direct clinical application is absent, strong numeracy skills are fundamental for nurses for tasks like medication dosage calculations, IV drip rate adjustments, and interpreting lab values, all of which require precision and accuracy.
What if the question involved fractions in a dosage calculation? A similar need for finding a common denominator and performing accurate arithmetic would be required, highlighting the importance of these foundational math skills.

How to Approach the Question

First, analyze the expression to identify the operations (addition, subtraction) and the terms involved (radicals).
Check each term to see if the radical can be simplified. A radical is simplified if the number under the root has no perfect square factors.
To simplify a radical like √18, find the largest perfect square that divides 18 (which is 9), and rewrite it as √(9 * 2).
Use the property √(a*b) = √a * √b to separate the terms, so √(9 * 2) becomes √9 * √2, which simplifies to 3√2.
After simplifying all terms, substitute them back into the original expression.
Combine the 'like terms' by adding or subtracting their coefficients. All terms with the same radical (e.g., √2) are like terms.

Concept Tested & Keywords

Concept Tested: Simplification of expressions involving radicals (square roots).
Stem keywords: Radicals, Square Roots, Simplification, Algebra
Lead-in keywords: Solve, Simplify

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Practise the full ESIC Nursing Officer 2016 (Shift -2)

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