To find where \( \sqrt{38} \) lies on a number line, we can first approximate \( \sqrt{38} \).
The perfect squares close to 38 are:
- \( 6^2 = 36 \)
- \( 7^2 = 49 \)
So, \( 6 < \sqrt{38} < 7 \).
Next, we can calculate \( \sqrt{38} \) more precisely:
Using a calculator or estimation, we find: \[ \sqrt{38} \approx 6.1644 \]
Now, let's determine between which pairs of rational numbers \( 6.1644 \) lies:
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Between 6.3 and 6.5: No, \( 6.1644 \) is less than 6.3.
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Between 19 and 19.2: No, \( 6.1644 \) is much less than 19.
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Between 18.9 and 19.1: No, \( 6.1644 \) is also less than this range.
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Between 6.1 and 6.2: Yes, \( 6.1644 \) is between 6.1 and 6.2.
The correct response is: Between 6.1 and 6.2.
1 answer