To determine why "It is between 5 and 6, probably closer to 5" is the correct answer regarding the square root of 28, let's analyze the numbers.
- Estimate the square root: We know that:
- \(5^2 = 25\)
- \(6^2 = 36\)
Since \(28\) lies between \(25\) and \(36\), we can conclude that \(\sqrt{28}\) must be between \(5\) and \(6\).
- Closer to 5 or 6?:
- To find out whether \(\sqrt{28}\) is closer to \(5\) or \(6\), we can observe the distances:
- The distance of \(28\) from \(25\): \[ 28 - 25 = 3 \]
- The distance of \(28\) from \(36\): \[ 36 - 28 = 8 \]
Since \(28\) is \(3\) units away from \(25\) (which corresponds to \(5\)) and \(8\) units away from \(36\) (which corresponds to \(6\)), it is clear that \(28\) is closer to \(5\) than to \(6\).
- Calculating the actual square root:
- The approximate value of \(\sqrt{28}\) can also be calculated as follows: \[ \sqrt{28} \approx 5.29 \] This value confirms that it is indeed between \(5\) and \(6\), and closer to \(5\).
Thus, the statement "It is between 5 and 6, probably closer to 5" is correct based on these calculations and observations.