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.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
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A0.168
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B1.68
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C16.8
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D168
Answer
Correct Answer: 1.68
Explanation
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:
Numerator: 3√5 = 3 × 2.24 = 6.72.Denominator: 2√5 − 0.48 = 2 × 2.24 − 0.48 = 4.48 − 0.48 = 4.00.Compute the quotient: 6.72 / 4.00 = 1.68.Verification / Alternative check:
Because the denominator simplifies to a neat integer (4), mental division confirms 1.68 exactly without rounding.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:
1.68