This is one way (there are loads):

1) Make an initial guess - I'll go with 150 here - if you square that you get 22500 which is too small.

2) Divide your square by the number 24336/150 = 162.23.

4) Now take the average between your initial guess and the new answer 162.24 + 150 = 312.24. 312.24/2 = 156.12

5) Repeat the procedure with your new result. 24336/156.12 = 155.88. Take the average again. (155.88 + 156.12)/2 = 156

6) Try the result 156*156= 24336 - (Hooray - a small cheer here for Ray)

Not all attempts at finding a square root will *converge *in just two steps like this example did - although if your initial guess is near, it will get pretty close in two or three. These sorts of *iterative* processes are much used in computational mathematics.