To determine \(\sqrt{42}\) to the nearest hundredth, Marlene should follow these steps using the provided table of squared values:
1. Review the Table:
- The table provides the squares of numbers ranging from 6.0 to 7.0 with increments of 0.1. Below are the relevant details:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
Square & 6.0^2 & 6.1^2 & 6.2^2 & 6.3^2 & 6.4^2 & 6.5^2 \\
\hline
Value & 36.0 & 37.2 & 38.4 & 39.7 & 41.0 & 42.3 \\
\hline
\end{array}
\][/tex]
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
Square & 6.6^2 & 6.7^2 & 6.8^2 & 6.9^2 & 7.0^2 \\
\hline
Value & 43.6 & 44.9 & 46.2 & 47.6 & 49.0 \\
\hline
\end{array}
\][/tex]
2. Locate the Interval for \(\sqrt{42}\):
- \(\sqrt{42}\) will be a number whose square is close to 42.0.
- From the table, \(6.4^2 = 41.0\) and \(6.5^2 = 42.3\).
3. Determine the Range for \(\sqrt{42}\):
- Since \(41.0 < 42 < 42.3\), it is clear that \(\sqrt{42}\) falls between 6.4 and 6.5.
4. Next Steps to Refine the Estimate:
- To find \(\sqrt{42}\) to more precision (nearest hundredth), Marlene should consider squares of numbers between 6.4 and 6.5.
Therefore, the correct approach for Marlene to find \(\sqrt{42}\) to the nearest hundredth is:
A. She should find the squares of numbers between 6.4 and 6.5.
