Multiple choice

Using the binomial expansion upto $3$ terms the approximate value of $(8.8)^{1/3}$ can be shown to be

  1. $2+\displaystyle \frac{67}{900}$
  2. $2+\displaystyle \frac{107}{900}$
  3. $2+\displaystyle \frac{58}{900}$
  4. $2+\displaystyle \frac{47}{900}$
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C Correct answer
Explanation

(8.8)^(1/3) = (8 + 0.8)^(1/3) = 2 * (1 + 0.1)^(1/3). Using binomial expansion (1+x)^n = 1 + nx + n(n-1)x^2/2: 2 * (1 + 1/3 * 0.1 + (1/3 * -2/3 * 0.01) / 2) = 2 * (1 + 0.0333 - 0.0011) = 2 + 0.0666 - 0.0022 = 2 + 0.0644. 58/900 is approx 0.0644.

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