Which square roots have a difference of about 0.5? (Number line)

To find which square roots have a difference of about 0.5, we can calculate the approximate values of each square root:

1. \( \sqrt{11} \approx 3.3166 \)
2. \( \sqrt{14} \approx 3.7420 \)
3. \( \sqrt{19} \approx 4.3589 \)
4. \( \sqrt{24} \approx 4.8989 \)

Now, we can find the differences between each pair of square roots:

• Difference between \( \sqrt{11} \) and \( \sqrt{14} \): \[ |\sqrt{14} - \sqrt{11}| \approx |3.7420 - 3.3166| \approx 0.4254 \]

• Difference between \( \sqrt{14} \) and \( \sqrt{19} \): \[ |\sqrt{19} - \sqrt{14}| \approx |4.3589 - 3.7420| \approx 0.6169 \]

• Difference between \( \sqrt{19} \) and \( \sqrt{24} \): \[ |\sqrt{24} - \sqrt{19}| \approx |4.8989 - 4.3589| \approx 0.5400 \]

• Difference between \( \sqrt{11} \) and \( \sqrt{19} \): \[ |\sqrt{19} - \sqrt{11}| \approx |4.3589 - 3.3166| \approx 1.0423 \]

• Difference between \( \sqrt{11} \) and \( \sqrt{24} \): \[ |\sqrt{24} - \sqrt{11}| \approx |4.8989 - 3.3166| \approx 1.5823 \]

• Difference between \( \sqrt{14} \) and \( \sqrt{24} \): \[ |\sqrt{24} - \sqrt{14}| \approx |4.8989 - 3.7420| \approx 1.1569 \]

Based on our calculations, the pairs of square roots that have a difference of about 0.5 are:

• \( \sqrt{11} \) and \( \sqrt{14} \) (approximately 0.4254)
• \( \sqrt{19} \) and \( \sqrt{24} \) (approximately 0.5400)

Therefore, the square roots \( \sqrt{11} \) and \( \sqrt{14} \) and \( \sqrt{19} \) and \( \sqrt{24} \) are the ones that have a difference of about 0.5.