Question

√27 x √243 x √12 / √125 x √18

Answer 1

that would be, assuming the usual carelessness with parentheses,
√(27*243*12 / 125*18) = 27/25 √30
or,
√(3^3*3^5*2^2*3 / 5^3*2*3^2)
= √(2^2*3^9 / 2*3^2*5^3)
= √(2*3^7/5^3)
= 3^3/5^2 √(2*3*5)
= 27/25 √30 or 27/5 √(6/5)

Answer 2

radical 27 = radical 9 times 3 so 3 radical 3
If you do this with all of the radicals, it makes the math a lot easier.

243 is 3 times 81 so 9 radical 3
12 = 4 times 3 so you have 2 radical 3