To determine what whole number and rational number \( \sqrt{10} \) is between, we need to find the approximate value of \( \sqrt{10} \).
Calculating \( \sqrt{10} \):
- We know that \( 3^2 = 9 \) and \( 4^2 = 16 \).
- Therefore, \( 3 < \sqrt{10} < 4 \).
To find a more precise approximate value, we can calculate the square root further:
\[ \sqrt{10} \approx 3.162 \]
Next, we round this to the nearest half:
- In terms of halves, \( 3.162 \) is closest to \( 3 \) and \( 3.5 \).
- Thus, \( \sqrt{10} \) rounded to the nearest half is \( 3.0 \).
Putting all this together, we find:
- The whole number \( \sqrt{10} \) is between is \( 3 \).
- The rational number to the nearest half that \( \sqrt{10} \) is between is \( 3.0\).
Thus, \( \sqrt{10} \) is between:
\[ 3 \text{ and } 3.5 \]
1 answer