Let's evaluate each element in the given table step by step.
### Top Row Elements:
1. [tex]\(\sqrt{3}\)[/tex]:
- The square root of 3 is approximately [tex]\(1.7320508075688772\)[/tex].
2. [tex]\(-\frac{24}{8}\)[/tex]:
- Calculate the fraction [tex]\(\frac{24}{8}\)[/tex]:
[tex]\[
\frac{24}{8} = 3
\][/tex]
- Now apply the negative sign:
[tex]\[
-3
\][/tex]
- The value is [tex]\(-3.0\)[/tex].
3. 0:
- This is simply [tex]\(0\)[/tex].
4. [tex]\(-4 . \overline{6}\)[/tex] (representing the recurring decimal [tex]\(-4.6666...\)[/tex]):
- The recurring decimal [tex]\(-4.6666...\)[/tex] can be represented as [tex]\(-4 - 0.6666...\)[/tex]:
[tex]\[
-4.6
\][/tex]
### Bottom Row Elements:
1. [tex]\(\pi\)[/tex]:
- The value of [tex]\(\pi\)[/tex] is approximately [tex]\(3.141592653589793\)[/tex].
2. [tex]\(\frac{\pi}{\pi}\)[/tex]:
- Since any non-zero number divided by itself is [tex]\(1\)[/tex], we get:
[tex]\[
\frac{\pi}{\pi} = 1
\][/tex]
3. [tex]\(-\sqrt{36}\)[/tex]:
- First, calculate the square root of 36:
[tex]\[
\sqrt{36} = 6
\][/tex]
- Now apply the negative sign:
[tex]\[
-6
\][/tex]
- The value is [tex]\(-6.0\)[/tex].
4. [tex]\(\frac{\sqrt{81}}{3}\)[/tex]:
- First, calculate the square root of 81:
[tex]\[
\sqrt{81} = 9
\][/tex]
- Now, divide by 3:
[tex]\[
\frac{9}{3} = 3
\][/tex]
- The value is [tex]\(3.0\)[/tex].
### Final Results:
[tex]\[
\begin{tabular}{l|l|l|l|}
\hline
1.7320508075688772 & -3.0 & 0 & -4.6 \\
\hline
3.141592653589793 & 1.0 & -6.0 & 3.0 \\
\hline
\end{tabular}
\][/tex]
