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Let x be any +ve number.
 If x=3q on squaring both sides
(x)2 = (3q)2 =9q2 =3(3q2) =3m
where m=3q2 m is also an integer
so, x2=3m 
If x= 3q+1 on squaring both sides
x2= (3q+1)2 x2=9q2+1+2*3q*1 x2= 3(3q2+2q)+1 x2=3m+1
where m =3q2+2q and is an integer (3m+1)
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