Which is the best approximation of \(\sqrt{1.5}(266)^{3/2}\) A) 1000 B)2700 C)3200 D) 4100 E)5300 Please, help.

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Which is the best approximation of \(\sqrt{1.5}(266)^{3/2}\) A) 1000 B)2700 C)3200 D) 4100 E)5300 Please, help.

Mathematics
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E
How?
I just plugged it into my calculator.

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And got 5313
Otherwise i'm not sure, sorry
Is there any other way to "approximation"??
without calculator?
Not that i know of, I hope someone else here can help you. good luck :)
Let it go. I have other problem which is more interesting than this one.
Where will compare the square of the problem to approximate to the square of the options: First, square the problem: $$ \left (\sqrt{1.5}266^{3/2} \right )^2\\ =1.5\times 266^3 $$ Each of the options, squared $$ \left (10^3\right )^2=10^2\times 10^4\\ 2700^2=27^210^4\\ 3200^2=32^210^4\\ 4100^2=41^210^4\\ 5300^2=53^210^4\\ $$ Now divide everything by \(10^4\) $$ =\cfrac{1.5\times 266^3}{10^4}\\ =\cfrac{1.5}{10}\cfrac{266^3}{10^3}\\ =.15\times26.6^3\\ =.15\times26.6\times26.6^2\\ =3.99\times26.6^2\\ \approx 4\times26.6^2\\ =2^226.6^2\\ =\left (2\times26.6\right )^2\\ \approx 53^2 $$ Which matches the last option after multiplying by \(10^4\)
WWWWWWWWWWWWWWoahhhhhhhhhhhh. How can you get this method? \(2700^2 =27^210^4\) it is true, but what is the logic on it?? where is the site to learn those tricks? please, please, please. @ybarrap
LOL - Here's the site - http://tinyurl.com/forloser66 Logic is to get rid of the radicals.

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