Work carefully with radicals and decimals: Given √5 = 2.24, evaluate (3√5) / (2√5 − 0.48) by simplifying numerator and denominator step by step.

Introduction / Context:This problem combines radicals with decimals. The key is to simplify the numerator and the denominator separately using the provided value for √5, and then perform a clean division. Such steps reinforce operational fluency with expressions containing roots and constants.

Given Data / Assumptions:

• √5 = 2.24 (use as given).
• Expression: (3√5) / (2√5 − 0.48).

Concept / Approach:First compute the numerator 3√5 and the linear combination in the denominator 2√5 − 0.48 by substituting √5 = 2.24. Once both are numeric, divide to get the final value. Keep exact steps to avoid decimal slips.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 0.168: Off by a factor of 10.
• 16.8 and 168: Off by factors of 10 and 100; these ignore the small denominator correction.

Common Pitfalls:

• Mistaking 2√5 − 0.48 as 2(√5 − 0.48) and distributing incorrectly.
• Arithmetic slip when subtracting 0.48 from 4.48.

Final Answer: