Let's approach ordering the given set from least to greatest one number at a time.
First Value
First, we have 2 14. To graph this value, we find 2 on the number line and move 14 steps in the positive direction.
Second Value
We could type sqrt(7) into a calculator to help us graph it. Or, we can compare it to the square root of two nearby perfect squares. We will show how to do this second option.
Now, we know that sqrt(7) lies between 2 and 3 on a number line. We also know that 7 is 3 steps to the right of 4 and 2 steps to the left of 9 on a number line.
4+3 →7+2 →9
Therefore, 7 is closer to 9 than it is to 4. With that in mind, we can approximate the location of sqrt(7).
Third Value
Next, let's plot 2.3. This number can be rewritten as the mixed number 2 13 to help us visualize how to graph it. We find 2 on the number line and move 13 steps in the positive direction.
Fourth Value
Similarly, we could type sqrt(8) into a calculator to help us graph it. Or, we can compare it to the square root of two nearby perfect squares.
Now, we know that sqrt(8) lies between 2 and 3 on a number line. We also know that 8 is 4 steps to the right of 4 and 1 step to the left of 9 on a number line.
4+4 →8+1 →9
Therefore, 8 is closer to 9 than it is to 4. With that in mind, we can approximate the location of sqrt(8).
Combining the Number Lines
Finally, let's combine all of our number lines into one.
Now, we can write the set in order from least to greatest.
{2 14, 2.3, sqrt(7), sqrt(8) }
