these are not university-level algebra questions.

for (1):

since everything in sight is positive we can square both sides without fear.

thus from:

18√18 = r√t, we have:

(324)(18) = r^{2}t

18^{3}= 5832 = r^{2}t.

clearly t < 18, or else r^{2}t > t^{3}> 5832. so t is some divisor of 18: 1,2,3,6,or 9.

if t = 1, r = √(5832), which is not an integer.

if t = 2, r = √(2916) = 54 <--this works ( (18)^{3}/2 = (9)(18)^{2}, which has square root 3*18 = 54).

if t = 3, r = √(1944), not an integer

if t = 6, r = √(972), not an integer

if t = 9, r = √(648), not an integer

(look at the prime factorization of 18 cubed)

so the only case where r and t are integers with r > t is t = 2, r = 54, hence rt = 108.

(2) 2x + 3x = 5x, the number of eggs in the basket must be a multiple of 5. 12 is not a multiple of 5.