Solving roots

blubla · #1 $Old$ October 7th, 2008, 07:55 PM

I have a problem here.

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?

icemanfan · #2 $Old$ October 7th, 2008, 08:03 PM

For the first series of roots, the square root of 3 is larger than the fifth root of 2, because $3^{(1/2)} > 2^{(1/2)} > 2^{(1/5)}$ . The tenth root of 5 is larger than the fifth root of 2 because $5^{(1/10)} > 4^{(1/10)} = (2^2)^{(1/10)} = 2^{(1/5)}$ . Since the square root of 5 is less than 3, we have

$3 > 5^{(1/2)}$

$3^{(1/2)} > 5^{(1/4)} > 5^{(1/10)}$ .

So the order from smallest to largest is $2^{(1/5)}, 5^{(1/10)}, 3^{(1/2)}$ .

blubla · #3 $Old$ October 7th, 2008, 08:50 PM

Thanks a lot for your help!