Start by approximating sqrt(23). Then multiply the result by - 1 and plot it on a number line.
Approximation: - 4.8 Number Line:
Practice makes perfect
To estimate - sqrt(23) to the nearest tenth we can consider sqrt(23) and multiply the result by - 1. We will find consecutive perfect squares around sqrt(23). Then we will compare the squares of the decimal numbers between them to the number under the root. We will do this one by one.
Finding Consecutive Whole Numbers
To find consecutive whole numbers around sqrt(23), let's narrow down our estimate by looking at nearby perfect squares. The two nearest perfect squares are 16 and 25.
We know that sqrt(23) is somewhere between 4 and 5. To approximate it to the nearest tenth we will use decimals between 4 and 5. Let's calculate the square of each number and compare them with 23.
Approximation
Square of Approximation
Comparison
4.1
4.1 * 4.1 = 16.81
Approximation is too low
4.2
4.2 * 4.2 = 17.64
Approximation is too low
4.3
4.3 * 4.3 = 18.49
Approximation is too low
4.4
4.4 * 4.4 = 19.36
Approximation is too low
4.5
4.5 * 4.5 = 20.25
Approximation is too low
4.6
4.6 * 4.6 = 21.16
Approximation is too low
4.7
4.7 * 4.7 = 22.09
Approximation is too low
4.8
4.8 * 4.8 = 23.04
Approximation is too high
We know that sqrt(23) is somewhere between 4.7 and 4.8. In order to estimate it to the nearest tenth, we need to find which square is closer. We will do this by finding the difference between 22.09 and 23, and 23 and 23.04.
22.09-0.91 ←23+0.04 →23.04
Because 23.04 is closer to 23, we know that sqrt(23.04) is closer to sqrt(23). Therefore, the nearest decimal number to sqrt(23) is 4.8, and the nearest decimal number to - sqrt(23) is - 4.8. Let's plot it on a number line.
