Compute the cube root: What is the cube root of 19,683?

Introduction / Context:Finding cube roots of perfect cubes can be done by recognizing patterns or recalling standard cubes. Here, 19,683 is a well-known perfect cube in aptitude exams.

Given Data / Assumptions:Number = 19,683; we seek n such that n^3 = 19,683.

Concept / Approach:Check nearby cubes: 20^3 = 8000, 25^3 = 15,625, 27^3 = 19,683, 30^3 = 27,000. The exact match is 27^3.

Step-by-Step Solution:

Verification / Alternative check:Prime factors: 19,683 = 3^9. Then cube root = 3^(9/3) = 3^3 = 27.

Why Other Options Are Wrong:25, 26, 28 and 24 cubes do not equal 19,683.

Common Pitfalls:Confusing with 28^3 = 21,952 or 26^3 = 17,576; quick memory of key cubes helps.

Final Answer:27