How do you add and multiply surds?

When you add and subtract surds, the numbers inside the square root must be the same. You add/ subtract the number outside the square root. e.g. 2√5 + 7√5 = 9√5, however 2√5 + 7√3 cannot be added. when you multiply and divide surds there is a different set of rules. If the 2 numbers inside the surd are the same, this creates a whole number. e.g √5 x √5 =5 if not, you multiply the numbers outside the surd together, the numbers inside the surd together and then simplify. e.g 3√5 x 6√3 = ~3x6= 18 ~ √(5x3) = √15 = 18√15 this is the same when dividing, first divide the whole numbers, then the surds.