ok so I get the general concept of surds and how you work simple ones out, but when getting to more difficult one how do you know what to divide by when simplifying or working out surds? you can divide the surd eg square root 200 by 2 but it can also be divided by 4 or 10 or 100 ect
Divide them by anything and you'll get to the same answer in the end Smaller factors will take more steps to simplify though - so you'll have to split even more surds So just go for the highest factors you can to save complications
In general, start by factoring out the largest square factor you can find. Repeat this until you are left with a number with no square factors within the square root.