To find the whole number and rational number to the nearest half that √30 lies between, we first need to estimate the value of √30.
We know that:
- \( \sqrt{25} = 5 \) (since \( 5^2 = 25 \))
- \( \sqrt{36} = 6 \) (since \( 6^2 = 36 \))
Since 30 is between 25 and 36, we have:
- \( 5 < \sqrt{30} < 6 \)
Next, we can use the process of approximation to find its value: Calculating \( \sqrt{30} \) gives us approximately \( 5.477 \).
Now, rounding \( 5.477 \) to the nearest half means we consider the nearest halves:
- The nearest halves around 5.477 are 5.5 and 5.
Thus, √30 is best described as being between 5 and 6, and the rational number to the nearest half is 5.5.
Therefore, we can fill in the blanks:
√30 is between 5 and 5.5.