Marlene is trying to estimate [tex]\sqrt{42}[/tex]. She uses this table of values:

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Square & [tex]$6.0^2$[/tex] & [tex]$6.1^2$[/tex] & [tex]$6.2^2$[/tex] & [tex]$6.3^2$[/tex] & [tex]$6.4^2$[/tex] & [tex]$6.5^2$[/tex] \\
\hline
Value & 36.0 & 37.2 & 38.4 & 39.7 & 41.0 & 42.3 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|c|c|c|}
\hline
Square & [tex]$6.6^2$[/tex] & [tex]$6.7^2$[/tex] & [tex]$6.8^2$[/tex] & [tex]$6.9^2$[/tex] & [tex]$7.0^2$[/tex] \\
\hline
Value & 43.6 & 44.9 & 46.2 & 47.6 & 49.0 \\
\hline
\end{tabular}

What should she do next to find [tex]\sqrt{42}[/tex] to the nearest hundredth?

A. She should find the squares of numbers between 6.4 and 6.5.

B. She should estimate that [tex]\sqrt{42}[/tex] is 6.50.

C. She should find the squares of numbers between 6.5 and 6.6.

D. She should find the average of 6.4 and 6.5.



Answer :

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.