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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 :

With some simplification, we note that: $\begin{eqnarray*} \sqrt{1.5}(266)^{3/2}=\sqrt{\frac{3}{2}}\cdot(266)^{3/2} & = & 266\sqrt{\frac{3\cdot 266}{2}} \\ & = & 266\sqrt{399}\approx266\cdot20\approx 5300. \end{eqnarray*}$
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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