Question

Using a number line, what whole number and rational number to the nearest half is 30−−√ between? Show your work. (1 point) 30−−√ is between and

Answer 1

what is it

Answer 2

To find the whole number and rational number to the nearest half that \(\sqrt{30}\) (30−−√) lies between, we need to calculate the approximate value of \(\sqrt{30}\).

1. **Estimate \(\sqrt{30}\)**:
- We know that \(\sqrt{25} = 5\) and \(\sqrt{36} = 6\).
- Therefore, \(\sqrt{30}\) is between 5 and 6.

2. **Narrowing Down**:
- To find a more precise value, we can use the average of 5 and 6:
\[
5.5^2 = 30.25 \quad (\text{too high})
\]
\[
5.4^2 = 29.16 \quad (\text{too low})
\]
- Hence, \(\sqrt{30}\) lies between 5.4 and 5.5.

3. **Nearest Half**:
- The nearest half would be 5.5 because \(\sqrt{30}\) is approximately 5.477.

In conclusion, the whole number and the rational number to the nearest half that \(\sqrt{30}\) is between are:

\[
\text{Between } 5 \text{ (whole number) and } 5.5 \text{ (rational number)}.
\]

Answer 3

I apologize if my previous response was unclear. Let’s clarify the bounds for \(\sqrt{30}\):

1. **Estimate \(\sqrt{30}\)**:
- We know that \(5^2 = 25\) and \(6^2 = 36\).
- Therefore, \(\sqrt{30}\) is between 5 and 6.

2. **Calculate \( \sqrt{30} \) more accurately**:
- A more precise value is approximately \(5.477\).

3. **Finding the nearest half**:
- The value of \(5.477\) is closer to \(5.5\) than it is to \(5.0\).

Thus, we can conclude:

**\(\sqrt{30}\) is between 5 and 5.5.**

To summarize:
- Whole number: **5**
- Rational number to the nearest half: **5.5**