To find an approximation of \( \sqrt{29} \) that can be used to estimate \( 3\sqrt{29} \) correct to two decimal places, we need to calculate \( 3 \times \sqrt{29} \) accurately.
First, the value of \( \sqrt{29} \) is approximately \( 5.38516 \) when calculated directly. We can round \( \sqrt{29} \) to \( 5.385 \) for a simpler calculation.
Now, we can compute \( 3\sqrt{29} \):
\[ 3 \times 5.385 = 16.155 \]
Now, rounding \( 16.155 \) to two decimal places gives us \( 16.16 \).
If we take a value with only three decimal places, say \( 5.385 \), it still keeps us accurate enough for two decimal place estimation of \( 3\sqrt{29} \).
Thus, the approximation of \( \sqrt{29} \) with the least number of decimal places that can be used to estimate \( 3\sqrt{29} \) correct to two decimal places is:
5.385