To compare \( \sqrt{42} \) and \( \sqrt{58} \), we can calculate their approximate values.
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Calculate \( \sqrt{42} \):
- Since \( 6^2 = 36 \) and \( 7^2 = 49 \), we know that \( \sqrt{42} \) is between 6 and 7.
- A better approximation can be found using a calculator, giving us: \[ \sqrt{42} \approx 6.48 \]
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Calculate \( \sqrt{58} \):
- Similarly, since \( 7^2 = 49 \) and \( 8^2 = 64 \), we know that \( \sqrt{58} \) is between 7 and 8.
- Using a calculator, we find: \[ \sqrt{58} \approx 7.62 \]
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Finding the approximate difference:
- Now, we compute the difference between the two values: \[ \sqrt{58} - \sqrt{42} \approx 7.62 - 6.48 = 1.14 \]
To express this difference in tenths, we can round \( 1.14 \) to the nearest tenth:
The approximate difference in tenths between \( \sqrt{58} \) and \( \sqrt{42} \) is \( \boxed{1.1} \).
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