 page four Let's look at what happens if you pick the wrong numbers:  How could you break up 48 such that the two numbers multiply to 48? There are lots of ways ... here's one:  Unfortunately, this won't help you simplify the radical, because neither the square root of 8 nor the square root of 6 is perfect, so you can't go any farther. Here's the proper way to do that question:  Notice that 16 times 3 is also 48, but in this case 16 is also a perfect square, so you can do its square root easily. Here's another one ... 
You've probably realized that we're leaving out the first step, where the '4 times 7' is under a single root sign. Also notice that we put the perfect root first. That way, when you work it out, the whole number will be in front of the left-over root. That's the proper way to write a mixed radical. Now let's examine what to do when the root is already part of a mixed radical: |