sqrt(18) + sqrt(162) / sqrt(72) = ?

Appeared in: OSSSC Nursing Officer-2023

Explanation

The correct approach is to first simplify each radical (square root) by factoring out the largest perfect square.
√18 simplifies to 3√2, √162 simplifies to 9√2, and √72 simplifies to 6√2.
The expression becomes (3√2 + 9√2) / (6√2), which simplifies to 12√2 / 6√2.
The common factor of √2 in the numerator and denominator cancels out, leaving 12 / 6.
The final result of the division is 2.

Option B: This answer may result from incorrect factoring of the radicals or an error in arithmetic. For example, incorrectly simplifying √18 as 2√3.
Option C: This is the simplified form of √18 alone. This error could occur if the student only performs the first step of the calculation or incorrectly cancels terms in the final fraction.
Option D: This answer likely arises from multiple errors in both simplifying the radicals and performing the final division. It does not follow a logical pathway from the original expression.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of radical expressions involving addition and division as background academic context rather than a clinical decision trigger.
While this is a pure mathematics question, the underlying skill of performing multi-step calculations with precision is critical in nursing.
Accurate calculation is paramount for patient safety in tasks like medication dosage calculation, IV drip rate setting, and interpreting lab results.
A small error in calculation, similar to mis-simplifying a radical, could lead to a significant medication error in a clinical setting.

How to Approach the Question

First, analyze the expression. Note that the way it is written (a + b / c) is ambiguous. However, since '2' is an option, it implies the structure is (a + b) / c. Assume the expression is (√18 + √162) / √72.
The strategy is to simplify each radical term before performing addition and division. Look for the largest perfect square that divides the number under the radical.
For √18, the largest perfect square is 9 (9 × 2 = 18). So, √18 = √9 × √2 = 3√2.
Apply the same process to √162 (81 × 2) and √72 (36 × 2).
Substitute these simplified forms back into the expression: (3√2 + 9√2) / 6√2.
Combine the like terms in the numerator and then perform the division, canceling common factors to find the final answer.

Concept Tested & Keywords

Concept Tested: Simplification of radical expressions involving addition and division.
Stem keywords: sqrt, radical, surds, simplification
Lead-in keywords: ?

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Practise the full OSSSC Nursing Officer-2023

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