Cube root of a very small decimal: Find the cube root of 0.000027.
Aptitude
Square Root and Cube Root
Difficulty: Easy
Choose an option
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A.3
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B.03
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C.003
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DNone of these
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E0.3
Answer
Correct Answer: .03
Explanation
Introduction / Context:We need the cube root of a small decimal. Recognize familiar cubes: 27 is 3^3, so 0.000027 relates directly to a scaled cube.
Given Data / Assumptions:
- Number: 0.000027 = 27 / 10^6.
- Use principal cube root (positive).
Concept / Approach:For positive a, ∛(a/10^n) = ∛a / 10^(n/3) when n is a multiple of 3. Here n = 6 is divisible by 3, which makes evaluation straightforward.
Step-by-Step Solution:
0.000027 = 27 / 10^6.∛(27 / 10^6) = ∛27 / ∛(10^6) = 3 / 10^2 = 3/100 = 0.03.Therefore, cube root = 0.03.Verification / Alternative check:(0.03)^3 = 27 / 10^6 = 0.000027, confirming the result exactly.
Why Other Options Are Wrong:
- .3^3 = 0.027, too large by a factor of 1000.
- .003^3 = 2.7e-8, far too small.
- “None of these” is not needed since .03 is present.
Common Pitfalls:Mixing square-root logic with cube roots or miscounting decimal-place triplets for cube roots.
Final Answer:.03