Shiv2016 wrote:
Expression II does not represent an integer because (82)* 82^1/2= 82^3/2 and 82^3= 2^3* 41^3 is not a perfect square. Regarding this last assertion, note that the square of any integer has the property that each of its distinct prime factors is repeated an even number of times.
(Explanation taken from official guide 2017)
\( 82*82^{(\frac{1}{2})}=82^{(1+\frac{1}{2})}=82^{\frac{3}{2} }=\sqrt{82^3} \)
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