The cube root of $.000216$ is

Concept & Strategy When finding the cube root of a decimal, first find the cube root of the non-zero integer part. Then, count the total number of decimal places in the original number. The final cube root will have exactly one-third the number of decimal places as the original perfect cube. Step-by-Step Solution * **Given number**: $0.000216$ * Count the decimal places: There are $6$ digits after the decimal point. * Find the cube root of the integer part. The significant integer part is $216$. We know from standard cubes that: $$6^3 = 216$$ * So, $\sqrt[3]{216} = 6$. * Determine correct decimal placement: Divide the number of original decimal places ($6$) by $3$ (since it is a cube root). $$6 \div 3 = 2$$ * The final cube root must have exactly $2$ decimal places. Applying this format to our integer root $6$ gives $0.06$. Exam Strategy & Shortcut Recognize $216$ as $6^3$ instantly. See the $6$ decimal places in the question. Apply the rule: the root must have $6/3 = 2$ decimal places. Immediately select $.06$ from the options without writing anything down. Common Pitfall Placing the decimal point incorrectly is the most common error. Students often select $.006$ by just visually carrying over zeros, or $.6$ by incorrectly confusing the decimal reduction rules of cube roots with square roots. Final Answer **Therefore, the correct answer is .06.**