Using a number line, what whole number and rational number to the nearest half is 30−−√
between?(1 point)
Responses
4.5 and 5
4.5 and 5
6 and 6.5
6 and 6.5
5.5 and 6
5.5 and 6
5 and 5.5
The first step is to calculate the approximate value of √30. The nearest perfect squares around 30 are 25 (which is 5 squared) and 36 (which is 6 squared). That means √30 is somewhere between 5 and 6. To know which whole number and rational number to the nearest half it is between, the calculation is as follows:
√25 < √30 < √36
5 < √30 < 6
Now, let's find out which halves are between 5 and 6. The halves are 5.5 and 6. So, √30 would be between these halves as well.
5 < √30 < 5.5 or 5.5 < √30 < 6
Now we can approximate the value of √30 to clarify the answer. √30 is approximately 5.477 (rounded to three decimal places), so it is closer to 5.5 on the number line. Thus, √30 falls between 5 and 5.5.
Therefore, the answer is:
5 and 5.5
This would be the range in which √30 is located on a number line between a whole number and a rational number to the nearest half.