If √24 is approximately equal to 4.898, then √(8/3) is nearly equal to?

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The core of the problem is to manipulate the expression √(8/3) to make use of the provided value for √24.
By multiplying the numerator and denominator of 8/3 by 3, we get (8 × 3) / (3 × 3) = 24/9. The expression becomes √(24/9).
Using the property of radicals √(a/b) = √a / √b, we can separate the expression into √24 / √9.
Substituting the given value √24 ≈ 4.898 and knowing √9 = 3, the calculation becomes 4.898 / 3.
The result of the division is approximately 1.63266..., which rounds to 1.633.

Option A: This value is incorrect and does not result from a logical application of the properties of square roots or the given numbers.
Option B: This value (1.333...) is the decimal equivalent of 4/3. This error might occur if one incorrectly approximates √24 as 4 before dividing by 3.
Option D: This value (2.666...) is the decimal equivalent of 8/3. This error arises from calculating the value inside the square root but forgetting to perform the square root operation itself.

Visual 1: Infographic - A step-by-step infographic showing the algebraic manipulation of √(8/3) to (√24)/3 and the final substitution and calculation. This visual would reinforce the logical flow of the solution.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of Surds/Radicals as background academic context rather than a clinical decision trigger.
This is a general aptitude and reasoning question, testing mathematical skills rather than clinical knowledge.
While not directly clinical, proficiency in basic mathematics is crucial for nurses for tasks like drug dosage calculations, IV drip rate adjustments, and interpreting patient data charts, where accuracy is critical for patient safety.
What if the question gave √6 ≈ 2.449? Then you could rewrite √(8/3) as √(16/6) = √16 / √6 = 4 / 2.449 ≈ 1.633. This shows that different manipulation paths can lead to the same result.

How to Approach the Question

First, identify the relationship between the number in the given value (24) and the numbers in the expression to be solved (8 and 3). Notice that 8 × 3 = 24.
Strategize how to transform the expression √(8/3) into a form that includes √24. This involves algebraic manipulation.
Multiply the fraction inside the square root by a form of 1 (in this case, 3/3) to create the desired term in the numerator: √(8/3 × 3/3) = √(24/9).
Apply the property of square roots √(a/b) = √a / √b to separate the numerator and denominator: √24 / √9.
Substitute the given value for √24 and the known value for √9.
Perform the final calculation and compare the result with the given options.

Concept Tested & Keywords

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Practise the full RRB Staff Nurse Mumbai-2015

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