Apply the sum-of-cubes identity with decimals: Evaluate [(2.247)^3 + (1.730)^3 + (1.023)^3 − 3*2.247*1.730*1.023] / [(2.247)^2 + (1.730)^2 + (1.023)^2 − (2.247*1.730) − (1.730*1.023) − (2.247*1.023)].

Introduction / Context:
The expression matches the well-known identity a^3 + b^3 + c^3 − 3abc = (a + b + c)(a^2 + b^2 + c^2 − ab − bc − ca). When the numerator and denominator are arranged in this exact pattern, the quotient simplifies dramatically to a + b + c, provided a + b + c ≠ 0.

Given Data / Assumptions:

• a = 2.247, b = 1.730, c = 1.023.
• Structure exactly matches the identity above.
• All arithmetic is exact (no rounding needed to reach the conclusion).

Concept / Approach:
Recognize the factorization and cancel the common factor (a^2 + b^2 + c^2 − ab − bc − ca) from numerator and denominator, leaving just a + b + c.

Step-by-Step Solution:

Verification / Alternative check:
Expanding the right-hand side (a + b + c)(a^2 + b^2 + c^2 − ab − bc − ca) reproduces the numerator, confirming the identity holds regardless of decimal values.

Why Other Options Are Wrong:
1.730 and 5.247 are partial sums; 4 is a rounded guess; 3 ignores the identity. Only 5 equals a + b + c.

Common Pitfalls:
Not spotting the identity and attempting long decimal expansions or mishandling negative signs in the −ab − bc − ca terms.

Final Answer:
5