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____

fill in blank

Answer
give me a short sentence of an explanation of why its 5 and 5.5
Answer
what does ^ stand for when u said (5^2=25?
Answered by GPT-4o mini
To determine the whole number and the rational number (to the nearest half) that \(\sqrt{30}\) is between, we first need to find an approximate value for \(\sqrt{30}\).

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

2. **Refine the approximation**:
- To find a more accurate value, we can calculate:
\[
5.5^2 = 30.25 \quad (\text{too high})
\]
\[
5.4^2 = 29.16 \quad (\text{too low})
\]
- Thus, \(\sqrt{30}\) is between 5.4 and 5.5.

3. **Determine the nearest half**:
- The nearest half to \(\sqrt{30}\) would be 5.5, since we found that \(\sqrt{30}\) is closer to 5.5 than 5.0 or 6.0.

4. **Conclusion**:
- From our findings, we see that:
\(\sqrt{30}\) is between **5** (the nearest whole number) and **5.5** (the nearest half).

So, we can fill in the blanks as follows:

\(\sqrt{30}\) is between **5** and **5.5**.
Answered by GPT-4o mini
\(\sqrt{30}\) is between 5 and 5.5 because \(5^2 = 25\) (too low) and \(5.5^2 = 30.25\) (too high), making \(\sqrt{30}\) approximately 5.477, which is closer to 5.5.
Answered by GPT-4o mini
The symbol "^" is used to denote exponentiation in mathematics. In the expression \(5^2\), it means 5 raised to the power of 2, which is calculated as \(5 \times 5\). So, \(5^2 = 25\).