Let's solve the problem of arranging the given expressions [tex]\(\sqrt{3}\)[/tex], [tex]\(3\sqrt{3}\)[/tex], and [tex]\(4\sqrt{3}\)[/tex] in ascending order.
1. Expression Identification:
- First, recognize the three expressions:
- [tex]\(\sqrt{3}\)[/tex]
- [tex]\(3\sqrt{3}\)[/tex]
- [tex]\(4\sqrt{3}\)[/tex]
2. Calculate the Numerical Values:
- We need to find the numerical values of each of these expressions.
- [tex]\(\sqrt{3} \approx 1.7320508075688772\)[/tex]
- [tex]\(3\sqrt{3} \approx 3 \times 1.7320508075688772 \approx 5.196152422706632\)[/tex]
- [tex]\(4\sqrt{3} \approx 4 \times 1.7320508075688772 \approx 6.928203230275509\)[/tex]
3. Arrange the Values in Ascending Order:
- Now, we will arrange the previously calculated numerical values:
- [tex]\(\sqrt{3} \approx 1.7320508075688772\)[/tex]
- [tex]\(3\sqrt{3} \approx 5.196152422706632\)[/tex]
- [tex]\(4\sqrt{3} \approx 6.928203230275509\)[/tex]
- Ordering these values from smallest to largest gives us the sequence:
- [tex]\(1.7320508075688772\)[/tex]
- [tex]\(5.196152422706632\)[/tex]
- [tex]\(6.928203230275509\)[/tex]
4. Conclusion:
- Therefore, when we arrange [tex]\(\sqrt{3}\)[/tex], [tex]\(3\sqrt{3}\)[/tex], and [tex]\(4\sqrt{3}\)[/tex] in ascending order, the result is:
[tex]\[
\sqrt{3}, 3\sqrt{3}, 4\sqrt{3}
\][/tex]
