Square root of a small decimal: Find an appropriate approximation for √0.064.
Aptitude
Square Root and Cube Root
Difficulty: Easy
Choose an option
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A0.8
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B0.08
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C0.008
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D0.252
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E0.32
Answer
Correct Answer: 0.252
Explanation
Introduction / Context:We estimate the square root of a small decimal. Because 0.064 is not a perfect square, we present a rounded value consistent with the options provided.
Given Data / Assumptions:
- Number: 0.064 = 64/1000.
- We want √0.064.
Concept / Approach:Compute √(64/1000) = 8/√1000 = 8/(10√10) = (4)/(5√10). Convert to decimal using √10 ≈ 3.1623.
Step-by-Step Solution:
√0.064 = (4)/(5√10) ≈ 4 / (5 * 3.1623) ≈ 4 / 15.8115 ≈ 0.25298.Rounded to three decimals, ≈ 0.253; the nearest listed option is 0.252.Verification / Alternative check:Square 0.252 ≈ 0.063504, very close to 0.064; with 0.253^2 ≈ 0.064009, straddling the true value.
Why Other Options Are Wrong:
- 0.8, 0.08, 0.008 are order-of-magnitude mismatches.
- 0.32 is also too large.
Common Pitfalls:Assuming 0.064 is close to 0.06 and guessing; compute using √(64/1000) to stay accurate.
Final Answer:0.252