To compare [tex]\(\pi\)[/tex] and [tex]\(\sqrt{8}\)[/tex], let's first understand their approximate numerical values.
1. Approximation of [tex]\(\pi\)[/tex]:
[tex]\(\pi \approx 3.14159\)[/tex]
2. Approximation of [tex]\(\sqrt{8}\)[/tex]:
To find [tex]\(\sqrt{8}\)[/tex], we can rewrite it as:
[tex]\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\][/tex]
We know that [tex]\(\sqrt{2} \approx 1.414\)[/tex]:
[tex]\[
2\sqrt{2} \approx 2 \times 1.414 = 2.828
\][/tex]
Now that we have the approximations:
- [tex]\(\pi \approx 3.14159\)[/tex]
- [tex]\(\sqrt{8} \approx 2.828\)[/tex]
By comparing these two values:
- [tex]\(3.14159\)[/tex] (value of [tex]\(\pi\)[/tex])
- [tex]\(2.828\)[/tex] (value of [tex]\(\sqrt{8}\)[/tex])
We see that:
[tex]\[
\pi > \sqrt{8}
\][/tex]
Therefore, the inequality statement comparing [tex]\(\pi\)[/tex] and [tex]\(\sqrt{8}\)[/tex] is:
[tex]\[
\pi > \sqrt{8}
\][/tex]
