1. Estimating Square Roots Using a Number Line

2. One effective model for approximating square roots is the number line method. To use this method it is important that you know all your square roots from 1 to 144.

3. Lets review . . . 1 x 1 = 1 7 x 7 = 49 2 x 2 = 4 8 x 8 = 64 3 x 3 = 9 9 x 9 = 81 4 x 4 = 16 10 x 10 = 100 5 x 5 = 25 11 x 11 = 121 6 x 6 = 36 12 x 12 = 144

4. How can we estimate the square root of 40? The first thing we must do is think about the perfect squares that are close to 40 – one perfect square that is less and one that is greater. In this case we must use 36 (6 x 6) and 49 (7 x 7). Now we will draw a number line that begins at 36 and ends at 49.

5. 36 37 38 39 40 41 42 43 44 45 46 47 48 49 We can now mark the perfect squares, 36 and 49, and their square roots on our number line. 36 37 38 39 40 41 42 43 44 45 46 47 48 49 6 x 6 7 x 7

6. ? 36 37 38 39 40 41 42 43 44 45 46 47 48 49 6 x 6 7 x 7 middle We are trying to estimate the square root of 40. If we look at 40 on the number line we see that it is closer to the perfect square 36. We can figure out that the middle of the number line is between 42 and 43 (42.5). This tells us that the square root of 40 is closer to 6 than 7. A good estimate for the square root of 40 is 6.3.

7. Estimate the square root of 58. ? 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 8 x 8 7 x 7 middle We know that the perfect squares nearest 58 are 49 and 64. We draw our number line using these numbers as our end points. We know the square root of 49 is 7 and the square root of 64 is 8. The middle of our number line is between 56 and 57 (56.5). 58 is closer to 64 than 49 so we know that the square root of 58 must be closer to 8. A good estimate for the square root of 58 is 7.7.

8. Now it’s time for you to practice estimating square roots using a number line on your own!