Mistake 2 - Simplifying Square Roots Incorrectly
A lot of times when simplifying square roots incorrectly students will say, "Oh, well I have an x squared. So that means if I took the square root of that then I that will be just x. And here's a 9, so the square root of the 9 is going to be 3. So that must be the answer." Well, actually, this is incorrect. Remember, we can only take away a square root or cancel out a square root if we have a perfect square underneath. So we have to be careful. What this x squared minus 9 really is is the difference of two perfect squares. It's not a perfect square as a whole. So, let's rewrite this a different way so that we can actually see that it's not a perfect square. So x squared minus 9 is just simply x plus 3 times x minus 3. Notice these are not actually the same factors. This one has a plus and this one has a minus. And this is a far as you can go with the square root. On the other hand, say if you had (what looks a little bit different) say if you had x minus 9 quantity squared. Now, this is actually a perfect square because you have x minus 9 times x minus 9. So, it's multiplied by itself twice. So that means since it's a perfect square we can say that x minus 9 squared, and if I take the square root of it, is just x minus 9.