 Welcome, everybody, to the Pythagorean Theorem, one of the most famous theorems of all time. Have your paper and pencil ready and follow along. I know you know the theorem a squared plus b squared equals c squared. These problems are going to be a little tougher as we want to put our answers in simplified radical form, and we want to make sure we know that c is the hypotenuse, and the hypotenuse in this case is 10, the longest side, always opposite the right angle. So we're going to substitute 10 in for c, and that's one of the most important things we have to notice is that 10 goes right in here for c squared. a and b are interchangeable as x and 5 are the legs, so I'm going to use x squared plus 5 squared equals 10 squared. And now I've got an algebra problem to solve, x squared plus 25 equals 100, subtract 25 from both sides, x squared equals 75. Now the final step is to put your answer in simplified radical form. So if I square root both sides, I'll get x equals the square root of 75. Now that can be simplified. There's a couple of different ways to do that. I'm going to do it by finding a square root that I know that multiplies to 75. So I'm going to choose 25 times 3. So I can break down 75 into the square root of 25 times the square root of 3. Simplifying that is 5 times the square root of 3. Or if you're really cool, you can say x equals 5 root 3. And that is the answer to the missing leg in this Pythagorean theorem problem.