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Number theory

Expert replies
by Fiver » Sat Oct 04, 2008 5:58 am
Which of the following expressions can be written as an integer?

I) (82^(1/2)+82^(1/2))^2

II) (82^(1/2))*82

III) (82^(1/2))*(82^(1/2))
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Source: — Problem Solving |

by Mani_mba » Sat Oct 04, 2008 6:41 am
I and III.
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Re: Number theory

by Morgoth » Sat Oct 04, 2008 9:38 am
Fiver wrote:Which of the following expressions can be written as an integer?

I) (82^(1/2)+82^(1/2))^2

II) (82^(1/2))*82

III) (82^(1/2))*(82^(1/2))

I) (82^(1/2)+82^(1/2))^2 = 2*(sqrt82)^2 = integer

II) (82^(1/2))*82 = 82*sqrt82 = not integer, but it this would have been (sqrt82)^82 it would have been integer.

III) (82^(1/2))*(82^(1/2)) = 82^2/2 = 82 = integer.
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Re: Number theory

by Fiver » Sun Oct 05, 2008 4:56 am
Morgoth wrote:
Fiver wrote: II) (82^(1/2))*82 = 82*sqrt82 = not integer, but it this would have been (sqrt82)^82 it would have been integer.
Thats exactly what I thought it was!!!
Thanks buddy.
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