Simplifying Roots

Video Transcript

"Let's look at simplifying roots. Any time you're dealing with a question, what that means by the way is, let's say you have square root of fifty and you're not allowed to use your calculator on a test, they don't want a decimal answer, so either the test or the teacher would say you're not allowed to use your calculator, or I want an exact answer, rather than a decimal. In either of those cases, you're going to simplify this root, rather than just get it on your calculator. Any time you have to do something like that, the best thing to do is start by making a list of the perfect squares. So, one square root is one, not really, doesn't matter till it's, two squares is four, three square, four square, five square, six square, seven square, eight square, nine square, ten square, that's pretty much what you need, if you're in like an advanced class or an honors class, you may need a couple more after ten, But, that's usually what you need. Now, the reason you want to put those on the side of your paper is because that's what we're going to use and you need to know which one. So, when you've got a root that you want to simplify, you take a look at the list and you look at the biggest number that might go into this number, that might divide into that number. It's too big, too big, too big, forty nine still too big, too big, twenty five, twenty five goes into fifty. What we're really asking is which perfect square goes into fifty. So, you go down the list, the highest one, you always want the highest one is twenty five. So, we re-write fifty as twenty five times two, cause fifty divided by twenty five is two. O.k, now, the reason we wanted that is because the square root of twenty five is actually five, that comes out of the square root side, square to twenty five simplifies two, or is equivalent to five. So, that comes out of the square root and goes on its own, it's now just a number, it's an integer and we're left with inside, square root of two. Square root of two doesn't simplify, nothing goes into it, it's a final answer. So, the simplified version of square root of fifty is five, square root of two. Let's take a look at a second example, so we're going to look at our list of numbers and say what's the highest perfect square that goes into forty eight, it's too high, too high, too much, too much, too much, twenty five, you can try it on your calculator, doesn't go evenly into forty eight, and then you try sixteen, forth eight divided by sixteen works, it goes in evenly. Forty eight divided by sixteen is three. So, we re-write forty eight as sixteen times three. The reason we did that is because square root of sixteen is that sixteen is a perfect square, so square root of sixteen is four. You take the sixteen out of the square root, it becomes four on its own, not underneath the square root but on its own, and the three is still there. So, square root of forth eight, the root of forty eight simplifies to be four, which is the square root of sixteen, times square root of three."