Determine the value of x when x^3 = 27.

Introduction / Context:
This is a direct cube equation that tests understanding of cube roots. Recognising basic cubes and their roots is important for many aptitude questions, especially those involving higher degree equations or simplifications.

Given Data / Assumptions:

• Equation: x^3 = 27.
• We look for the real value of x.
• Options: 1, 3, 9, 12.

Concept / Approach:
To solve x^3 = 27, we find the cube root of 27. Since 3^3 = 27, 3 is the real cube root. This is a basic fact that should be memorised: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, and so on. Among the options, we pick the value whose cube equals 27.

Step-by-Step Solution:
Step 1: Start with the equation x^3 = 27.Step 2: Take the cube root of both sides: x = cube root of 27.Step 3: Recall that 3^3 = 3 * 3 * 3 = 9 * 3 = 27.Step 4: Therefore cube root of 27 is 3.Step 5: So the solution is x = 3.

Verification / Alternative check:
We can verify by substituting x = 3 back into the equation. Compute 3^3 = 27, which matches the right hand side. None of the other options yield 27 when cubed.

Why Other Options Are Wrong:

• 1: 1^3 = 1, not 27.
• 9: 9^3 = 729, much larger than 27.
• 12: 12^3 = 1728, again much larger than 27.

Common Pitfalls:
Some students confuse square roots and cube roots, and might mistakenly think of 27 as 3^2 or as 9^2. It is essential to remember the basic cube values for small integers to avoid such mistakes.

Final Answer:
The value of x satisfying x^3 = 27 is 3.