 page two Let's look at the square root of 32 again:  We're going to exchange 32 for a pair of numbers that multiply to 32. There are several possibilities. Here's the one we're going to pick: 
We picked 16 and 2 for a reason. 16 is the biggest perfect square that's a factor of 32. What does this mean? Well, you already know that square roots multiply together. So we can do this: 
And now, because 16 is a perfect square, its root is 4:  What we've done is change the square root of 32 into 'four times the square root of 2': is equal to 
Because the number under the radical sign is smaller, the root is considered to be simpler. Of course, not all square roots can be simplified. Here's one that won't simplify:  (There is no pair of factors of 30 such that one of them is a perfect square) Let's do another example ... |