To determine the correct arrangement of the numbers [tex]\(\sqrt{5}\)[/tex], [tex]\(\sqrt{2}\)[/tex], and [tex]\(\sqrt{3}\)[/tex] in ascending order, we consider their approximate decimal values:
- [tex]\(\sqrt{2}\)[/tex] is approximately [tex]\(1.414\)[/tex]
- [tex]\(\sqrt{3}\)[/tex] is approximately [tex]\(1.732\)[/tex]
- [tex]\(\sqrt{5}\)[/tex] is approximately [tex]\(2.236\)[/tex]
By comparing these values:
1. The smallest value among these is [tex]\(\sqrt{2} \approx 1.414\)[/tex].
2. The next smallest value is [tex]\(\sqrt{3} \approx 1.732\)[/tex].
3. The largest value is [tex]\(\sqrt{5} \approx 2.236\)[/tex].
Hence, the ascending order of [tex]\(\sqrt{5}\)[/tex], [tex]\(\sqrt{2}\)[/tex], and [tex]\(\sqrt{3}\)[/tex] is:
[tex]\[
\sqrt{2} < \sqrt{3} < \sqrt{5}
\][/tex]
So the correct answer is:
a. [tex]\(\sqrt{2}, \sqrt{3}, \sqrt{5}\)[/tex]
