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Sunday, 28 August 2011

Math GRE - #27

Which of the following is the best approximation of $\sqrt{1.5}(266)^{3/2}$?

  1. 1000
  2. 2700
  3. 3200
  4. 4100
  5. 5300

Solution :

Choice 5 is the answer.

With some simplification, we note that: \[\begin{eqnarray*}
\sqrt{1.5}(266)^{3/2}=\sqrt{\frac{3}{2}}\cdot(266)^{3/2} & = & 266\sqrt{\frac{3\cdot 266}{2}} \\
& = & 266\sqrt{399}\approx266\cdot20\approx 5300.
Those of us familiar with Taylor series may try approximations with calculus, however this question teaches us that too much knowledge may be a little bit dangerous if misapplied. And that most of the time, there are simpler solutions than you'd think.


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