Multiple choice

Find the approximate value of $\displaystyle \left ( 0.009 \right )^{1/3}$.

  1. $0.208$
  2. $0.108$
  3. $0.205$
  4. $0.204$
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A Correct answer
Explanation

The cube root of 0.009 is approximately 0.208 because 0.208 * 0.208 * 0.208 is approximately 0.0089989.

AI explanation

Rewrite the expression as the fraction 9 divided by 1000 raised to the power of 1 divided by 3, which separates into the cube root of 9 divided by the cube root of 1000. Since the cube root of 1000 is 10, the expression simplifies to the cube root of 9 divided by 10. Using linear approximation around the perfect cube 8, the cube root of 9 is approximately 2 plus 1 divided by 12, which is 2.0833, and dividing this by 10 gives 0.208.

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