To find the approximate value of the square root of 58 and determine its position between two rational numbers on a number line, we can follow these steps:
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Calculate \(\sqrt{58}\):
The square root of 58 is approximately 7.616 (you can use a calculator for this value). -
Identify rational numbers:
We need to find two rational numbers between which this value lies. Since \(\sqrt{58} \approx 7.616\), we can consider the whole numbers around this value. The closest whole numbers are 7 and 8. -
Determine the nearest half:
The number 7.616 falls between 7.5 and 8. Since we're looking for the nearest half, it is closer to 7.5 than to 8.
Therefore, we can conclude that \(\sqrt{58}\) is between the rational numbers 7.5 and 8.
On a number line, you can represent this as:
7.5 < \(\sqrt{58}\) < 8