To find a decimal approximation for \(\sqrt{10}\) without exceeding 10, we can calculate its value.
Using a calculator, we find:
\[ \sqrt{10} \approx 3.162 \]
This value does not exceed 10 and is a good approximation for \(\sqrt{10}\).
If you need a rough estimate without a calculator, you might know that \(\sqrt{9} = 3\) and \(\sqrt{16} = 4\), so \(\sqrt{10}\) must be between 3 and 4.
Also, you can approximate further:
\[ 3.1^2 = 9.61 \quad \text{and} \quad 3.2^2 = 10.24 \]
So, \(\sqrt{10}\) is slightly greater than 3.1 but less than 3.2.
A common exact approximation used is:
\[ \sqrt{10} \approx 3.16 \]
Thus, the closest decimal approximation for \(\sqrt{10}\) without exceeding 10 is approximately:
\(\mathbf{3.162}\) (or rounded to \(\mathbf{3.16}\) if needed).
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