Which is the number when squared is one third of its cube?

Appeared in: BSF Staff Nurse - 2015

Explanation

The question asks to identify a number where its square equals one-third of its cube.
Let the number be 'N'. The condition is N² = N³/3.
For the number 3, its square is 3² = 9.
The cube of 3 is 3³ = 27.
One-third of its cube is 27 / 3 = 9.
Since 9 = 9, the number 3 satisfies the condition.

Option A: For the number 2, its square is 4, but one-third of its cube is 8/3 ≈ 2.67. These values are not equal.
Option C: For the number 4, its square is 16, but one-third of its cube is 64/3 ≈ 21.33. These values are not equal.
Option D: For the number 1, its square is 1, but one-third of its cube is 1/3 ≈ 0.33. These values are not equal.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving an algebraic word problem involving exponents (squares and cubes) as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and logical reasoning, which are foundational skills for nurses.
Accurate mathematical skills are critical in clinical practice for tasks such as calculating drug dosages, IV drip rates, and interpreting lab results.
A mistake in a simple calculation can have serious patient safety consequences.

How to Approach the Question

First, deconstruct the word problem into a mathematical relationship. Identify what 'squared' and 'one-third of its cube' mean.
Translate the sentence into an equation: Let the number be 'x'. The equation is x² = (1/3)x³.
Since the options are simple whole numbers, the easiest approach is to test each one.
For each option, calculate its square and its cube.
Then, calculate one-third of the cube.
Compare the result of the square with the result of one-third of the cube. The option where these two values are equal is the correct answer.

Concept Tested & Keywords

Concept Tested: Solving an algebraic word problem involving exponents (squares and cubes).
Stem keywords: number, squared, one third, cube
Lead-in keywords: Which is

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Practise the full BSF Staff Nurse - 2015

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