To determine which square roots have a difference of about 0.5, we can approximate each square root:
- \(\sqrt{11} \approx 3.32\)
- \(\sqrt{14} \approx 3.74\)
- \(\sqrt{19} \approx 4.36\)
- \(\sqrt{24} \approx 4.90\)
Now we can calculate the differences:
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Difference between \(\sqrt{11}\) and \(\sqrt{19}\): \[ |\sqrt{19} - \sqrt{11}| \approx |4.36 - 3.32| \approx 1.04 \quad (\text{not close to } 0.5) \]
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Difference between \(\sqrt{19}\) and \(\sqrt{24}\): \[ |\sqrt{24} - \sqrt{19}| \approx |4.90 - 4.36| \approx 0.54 \quad (\text{close to } 0.5) \]
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Difference between \(\sqrt{11}\) and \(\sqrt{14}\): \[ |\sqrt{14} - \sqrt{11}| \approx |3.74 - 3.32| \approx 0.42 \quad (\text{close to } 0.5) \]
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Difference between \(\sqrt{14}\) and \(\sqrt{19}\): \[ |\sqrt{19} - \sqrt{14}| \approx |4.36 - 3.74| \approx 0.62 \quad (\text{not close to } 0.5) \]
The pairs that have a difference close to 0.5 are:
- \(\sqrt{19}\) and \(\sqrt{24}\) (about 0.54)
- \(\sqrt{11}\) and \(\sqrt{14}\) (about 0.42)
Therefore, the correct responses are both options:
- 11−−√ and 14−−√ (square root of 11 and square root of 14)
- 19−−√ and 24−−√ (square root of 19 and square root of 24)
However, if you need to choose only one based on the higher relevance to the threshold of 0.5, the best response would be:
\( \sqrt{19} \) and \( \sqrt{24} \) (square root of 19 and square root of 24).
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