Discussion
What is the cube root of 0.000064?
Answer: B
Correct answer: 0.04
Write the number as a fraction of powers of ten: \[ 0.000064 = \frac{64}{1000000} = \frac{4^{3}}{100^{3}}. \] Taking the cube root of numerator and denominator separately, \[ \sqrt[3]{0.000064} = \frac{4}{100} = 0.04. \] The reliable method with decimals is to count places. A cube root divides the number of decimal places by three, so six decimal places become two. Since \( \sqrt[3]{64} = 4 \), the answer is 4 with two decimal places, which is 0.04. The same rule applied to a square root halves the decimal places: \( \sqrt{0.0064} = 0.08 \), because four places become two and \( \sqrt{64} = 8 \). Checking is quick: \( 0.04^{3} = 0.04 \times 0.04 \times 0.04 = 0.000064 \). Miscounting the places is the only real difficulty, and the distractors are all off by exactly one.
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