Using a number line, what whole number and rational number to the nearest half is 30−−√
between? (1 point)
To find the whole number and rational number to the nearest half that is between $30$ and $\sqrt{30},$ we can approximate the value as follows:
$\sqrt{30} \approx 5.5.$
Since $5$ is the whole number closest to $5.5,$ and $5$ can also be expressed as $\frac{10}{2},$ the whole number and rational number to the nearest half that is between $30$ and $\sqrt{30}$ is $\boxed{5}.$
To determine which whole number and rational number to the nearest half lies between 30−−√ on a number line, we can compare it with the nearest whole numbers.
Let's find the whole numbers on either side of 30−−√:
We know that the square root of 30 is between 5 and 6 because 5^2 = 25 < 30, and 6^2 = 36 > 30.
So, the nearest whole numbers are:
To the left of 30−−√: 5
To the right of 30−−√: 6
Now, let's find the rational numbers to the nearest half:
To the left of 30−−√: The square root of 30 is approximately between 5 and 6. To find the value between, we can add 0.5 to 5:
5 + 0.5 = 5.5
To the right of 30−−√: We can subtract 0.5 from 6:
6 - 0.5 = 5.5
Therefore, on a number line, the whole number and rational number to the nearest half between 30−−√ is 5.5.