The Square Root Property Before we learn about the square root property, let’s go over how to solve the problem given to you last week. Solution to Last Week’s Problem In last week’s post we went over how to complete the square on an expression of the form x2 + bx You can see that post here: Completing the Square I also promised to provide a solution to the following question: x2 – 8x If the method of completing the square is used to rewrite the expression above in the form (x – h)2 + k, then what is the value of h – k ? Solution: We divide –8 by 2 to get –4, and then square this number to get 16. So we add and subtract 16 to the given expression to get x2 – 8x = x2 – 8x + 16 – 16 = (x – 4)2 – 16 So h = 4, k = –16, and therefore h – k = 4 –(–16) = 4 + 16 = 20. The Square Root Property The square root property says that if x2 = a2, then x = ±a. Example 1: The equation x2 = 9 has the two solutions x = 3 and x = –3. Important note: Using the square root property is different from taking a square root. We apply the square root property to an equation of the form x2 = a2 to get two solutions, whereas when we take the positive square root of a number we get just one answer. For example when we take the positive square root of 9 we get 3, but when we apply the square root property to the equation x2 = 9, we have seen that we get the two solutions x = 3 and x = –3. Example 2: (x – 3)2 = 2 What is the solution set of the above equation? (A) {1, 5} (B) {3 + √2} (C) {3 – √2, 3 + √2} (D) The equation has no solutions. I will provide you with the solution to this problem next week. In the meantime feel free to try this problem yourself and post your own solution in the comments. If you liked this article, please share it with your Facebook friends: Comments comments