To determine the whole number and the rational number to the nearest half that \( \sqrt{40} \) is between, we first need to calculate \( \sqrt{40} \).
We can simplify \( \sqrt{40} \) as follows: \[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Now, we need to find the approximate value of \( \sqrt{10} \). The square root of 10 is roughly 3.162. Therefore, we can multiply by 2: \[ \sqrt{40} \approx 2 \times 3.162 \approx 6.324 \]
Now, let's identify the whole number around this value. The whole number immediately below \( 6.324 \) is 6, and the whole number above it is 7. Thus, \( \sqrt{40} \) is between the whole numbers 6 and 7.
Next, we need to find a rational number to the nearest half. The nearest half around 6.324 is 6.5.
Therefore, summarizing all this, we can say that: \[ \sqrt{40} \text{ is between } 6 \text{ and } 7, \text{ and the nearest half is } 6.5. \]
So, we have: \(\sqrt{40}\) is between 6 and 7.
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