Multiple choice

The approximate value of $\sqrt [3]{-0.99}$ is ______.

  1. $-0.9967$
  2. $0.9776$
  3. $-1.0033$
  4. $-1$
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A Correct answer
Explanation

Using the binomial approximation (1+x)^n approx 1+nx for small x. (-1 + 0.01)^(1/3) = -1 * (1 - 0.01)^(1/3) approx -1 * (1 - 0.01/3) = -1 * (1 - 0.00333) = -0.99666.

AI explanation

We can rewrite the expression as $-\sqrt[3]{0.99} = -(1 - 0.01)^{1/3}$. Using the approximation $(1 - x)^n \approx 1 - nx$ for small $x$, we calculate $-\left[1 - \frac{1}{3}(0.01)\right] = -(1 - 0.0033)$. This simplifies to $-0.9967$, which is the approximate value.

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