Loser66 one year ago Which is the best approximation of $$\sqrt{1.5}(266)^{3/2}$$ A) 1000 B)2700 C)3200 D) 4100 E)5300 Please, help.

1. MeowLover17

E

2. Loser66

How?

3. MeowLover17

I just plugged it into my calculator.

4. MeowLover17

And got 5313

5. MeowLover17

Otherwise i'm not sure, sorry

6. Loser66

Is there any other way to "approximation"??

7. Loser66

without calculator?

8. MeowLover17

Not that i know of, I hope someone else here can help you. good luck :)

9. Loser66

Let it go. I have other problem which is more interesting than this one.

10. ybarrap

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 $$10^4$$

11. Loser66

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

12. ybarrap

LOL - Here's the site - http://tinyurl.com/forloser66 Logic is to get rid of the radicals.

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