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 Zets October 7th, 2008 05:52 PM

Solving roots

I have a problem here.
http://img80.imageshack.us/img80/9990/rootio6.jpg
http://img80.imageshack.us/img80/rootio6.jpg/1/w345.png

This is a homework were I have to solve the roots and order them from greatest to least. But specifically, my problem is with the roots greater than square. I have no idea how to solve them. I know how to solve square roots, but roots greater than square seem to have different way of solving, and I can't solve them. No idea. Can anyone please help me with these?

 Dave October 7th, 2008 07:44 PM

Re: Solving roots

The order will be the same if you raise the power of each by the same amount. Express as fractional exponents first.

I'll help with the first...

$\sqrt 3 ,\sqrt[5]{2},\sqrt[{10}]{5}= 3^{{\textstyle{1 \over 2}}} ,2^{{\textstyle{1 \over 5}}} ,5^{{\textstyle{1 \over {10}}}}$

multiply by the LCD of the exponents. That would be 10.

$3^{{\textstyle{{10} \over 2}}} ,2^{{\textstyle{{10} \over 5}}} ,5^{{\textstyle{{10} \over {10}}}}= 3^5 ,2^2 ,5^1$

Now it should be obvious.

 skipjack October 8th, 2008 04:05 AM

Once you have converted a fifth root (for example) into an exponent of 1/5, just put 2^(1/5) (for example) into Google to find its value. Finally, order the resulting values.

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