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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}?
1000
2700
3200
4100
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.
\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.
2 comments:
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This webpage is LaTeX enabled. To type in-line formulae, type your stuff between two '$'. To type centred formulae, type '\[' at the beginning of your formula and '\]' at the end.
Another technique is to roughly approximate the square of the given formula, which will be slightly greater than
[; 1.5 * 250^3 \sim 1.5 * 16000000 = 24000000.;]
The square root of that is nearly 5000, so the answer will be 5300.
@686935176283448507.0
Hmm but you rounded up when you approximated 1.5*16000000 and then you rounded up again when you approximated 24000000 as 25000000 so I'm not entirely convinced.
Hmm but you rounded up when you approximated 1.5*16000000 and then you rounded up again when you approximated 24000000 as 25000000 so I'm not entirely convinced.
2 comments:
Post a Comment
This webpage is LaTeX enabled. To type in-line formulae, type your stuff between two '$'. To type centred formulae, type '\[' at the beginning of your formula and '\]' at the end.
[; 1.5 * 250^3 \sim 1.5 * 16000000 = 24000000.;]
The square root of that is nearly 5000, so the answer will be 5300.
Hmm but you rounded up when you approximated 1.5*16000000 and then you rounded up again when you approximated 24000000 as 25000000 so I'm not entirely convinced.
Another technique is to roughly approximate the square of the given formula, which will be slightly greater than
[; 1.5 * 250^3 \sim 1.5 * 16000000 = 24000000.;]
The square root of that is nearly 5000, so the answer will be 5300.
Hmm but you rounded up when you approximated 1.5*16000000 and then you rounded up again when you approximated 24000000 as 25000000 so I'm not entirely convinced.
Post a Comment