If $\sqrt{24}$ is approximately equal to 4.898, then $\sqrt{\frac{8}{3}}$ is nearly equal to

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The core task is to manipulate the expression √(8/3) to utilize the given value of √24.
By multiplying the numerator and denominator inside the square root by 3, the expression becomes √((8×3)/(3×3)) = √(24/9).
Using the property √(a/b) = √a / √b, this simplifies to √24 / √9.
Substituting the given value √24 ≈ 4.898 and the known value √9 = 3, we get 4.898 / 3.
The division results in 1.6326..., which rounds to 1.633.

Option A: This value is incorrect and likely results from a significant calculation error or an incorrect simplification method.
Option B: This value (1.333...) is the decimal equivalent of 4/3. It might be obtained by an incorrect simplification, such as taking the square root of 8 as approximately 4 and then dividing by 3, which is mathematically flawed.
Option D: This value (2.666...) is approximately the value of the fraction 8/3 itself, not its square root. The user may have forgotten to perform the final square root operation.

Visual 1: No visual is required for this question as it is a straightforward mathematical calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of Surds (Square Roots) as background academic context rather than a clinical decision trigger.
While not a direct clinical question, this type of problem assesses the basic mathematical aptitude and logical reasoning required for various nursing tasks.
Accurate calculation skills are critical for medication dosage calculations, IV drip rate adjustments, and interpreting patient data, where a simple mathematical error can have serious patient safety consequences.
What if the problem was to find √(3/8)? The same principle would apply: √(3/8) = √(3×3 / 8×3) = √9 / √24 = 3 / 4.898 ≈ 0.612.

How to Approach the Question

First, carefully read the question to understand what is given (√24 ≈ 4.898) and what needs to be found (the value of √(8/3)).
Analyze the expression you need to solve, √(8/3), and look for a way to relate it to the given information, √24.
Formulate a strategy: Modify the expression √(8/3) by multiplying the numerator and denominator by a number that will result in 24 in the numerator.
Execute the plan: √(8/3) = √((8×3)/(3×3)) = √(24/9).
Simplify the resulting expression using the rules of surds: √(24/9) = √24 / √9.
Substitute the known values (√24 ≈ 4.898 and √9 = 3) and perform the final calculation: 4.898 / 3.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Ahmedabad-2015

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