Question

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Answer 1

To find the whole number and the rational number (to the nearest half) that \( \sqrt{30} \) is between, we'll first need to calculate the approximate value of \( \sqrt{30} \).

1. Calculate \( \sqrt{30} \): \[ \sqrt{30} \approx 5.477 \]

2. Determine the whole number: The whole numbers around \( 5.477 \) are:

   • The greatest whole number less than \( 5.477 \) is \( 5 \).
   • The smallest whole number greater than \( 5.477 \) is \( 6 \).

   Therefore, \( \sqrt{30} \) is between the whole numbers \( 5 \) and \( 6 \).

3. Determine the rational number to the nearest half: The nearest half surrounding \( 5.477 \) would be:

   • The nearest half below \( 5.477 \) is \( 5.5 \).
   • The nearest half above \( 5.477 \) is \( 5.0 \).

   Since \( 5.477 \) is closer to \( 5.5 \) than to \( 5.0 \), we round \( \sqrt{30} \) to the nearest half: \[ \text{Nearest half} = 5.5 \]

4. Conclusion: Therefore, we can conclude that: \[ \sqrt{30} \text{ is between the whole numbers } 5 \text{ and } 6, \text{ and the rational number to the nearest half is } 5.5. \]

So the final statement can be written as: \[ \sqrt{30} \text{ is between } 5 \text{ and } 6, \text{ and } 5.5. \]

Answer 2

not so many unnecessary symbols and words

Answer 3

Sure! Here’s a more concise response:

1. Calculate \( \sqrt{30} \): \[ \sqrt{30} \approx 5.477 \]

2. Whole numbers:

   • Between 5 and 6.

3. Nearest half:

   • Round \( 5.477 \) to \( 5.5 \).

Final answer: \[ \sqrt{30} \text{ is between } 5 \text{ and } 6, \text{ and } 5.5. \]