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
II) (82^(1/2))*82
III) (82^(1/2))*(82^(1/2))
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Number theory
Source: Beat The GMAT — Problem Solving |
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.
Morgoth wrote:Thats exactly what I thought it was!!!Fiver wrote: II) (82^(1/2))*82 = 82*sqrt82 = not integer, but it this would have been (sqrt82)^82 it would have been integer.
Thanks buddy.
