Question

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

Answer 1

E

Answer 2

How?

Answer 3

I just plugged it into my calculator.

Answer 4

And got 5313

Answer 5

Otherwise i'm not sure, sorry

Answer 6

Is there any other way to "approximation"??

Answer 7

without calculator?

Answer 8

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

Answer 9

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

Answer 10

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 \(10^4\)

Answer 11

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

Answer 12

LOL - Here's the site - http://tinyurl.com/forloser66

Logic is to get rid of the radicals.