To calculate the geometric mean we need to first of all multiply 24 and 32 and take the square root of it (i.e. 24*32 is 768, √768 is 27.712.....). However, in this case, we need to represent the answer in a simplified surd. To do this we need to find the highest possible perfect square that is below 768. Here it is 27 because 27*27 equals 729. Now we can go ahead and subtract 768 by 729. We get 39. So now we got two different surds. √729 and √39. We can simplify the √729 to 27. Thus our answer is the combination of both 27*√39 or 27√39.
