To find \(\sqrt{40}\) and determine the whole number and the rational number to the nearest half, we first calculate \(\sqrt{40}\).
We can simplify \(\sqrt{40}\) as follows:
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Next, we need to estimate \(\sqrt{10}\). Knowing that \(3^2 = 9\) and \(4^2 = 16\), we can conclude:
\[ 3 < \sqrt{10} < 4 \]
To be more precise, we can approximate \(\sqrt{10}\) to about \(3.162\). Therefore:
\[ \sqrt{40} \approx 2 \times 3.162 = 6.324 \]
Now we can identify the whole number and the rational number to the nearest half:
- The whole number part is \(6\) (since \(6.324\) is between \(6\) and \(7\)).
- To round to the nearest half, we see that \(6.324\) is closer to \(6.5\) than to \(6\) or \(7\).
Thus, the answers are:
- Whole number: \(6\)
- Rational number to the nearest half: \(6.5\)
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