Let's solve the given mathematical expression step-by-step:
### Part 1: Calculate [tex]\(\frac{3}{7} + 0\)[/tex]
1. Identify the terms involved:
- [tex]\(\frac{3}{7}\)[/tex]
- [tex]\(0\)[/tex]
2. Perform the addition:
- Adding [tex]\(0\)[/tex] to any number leaves the number unchanged.
- Therefore, [tex]\(\frac{3}{7} + 0 = \frac{3}{7}\)[/tex]
3. Simplify the fraction:
- The fraction [tex]\(\frac{3}{7}\)[/tex] is already in its simplest form.
- Converting [tex]\(\frac{3}{7}\)[/tex] to a decimal, we get approximately [tex]\(0.42857142857142855\)[/tex].
### Part 2: Calculate [tex]\(\sqrt[6]{6} + \frac{19}{21}\)[/tex]
1. Evaluate the sixth root of 6:
- [tex]\(\sqrt[6]{6}\)[/tex] is a root which can be written as [tex]\(6^{\frac{1}{6}}\)[/tex].
- This value is a real number that can be approximately calculated as [tex]\(1.8143608829626605\)[/tex].
2. Evaluate the fraction [tex]\(\frac{19}{21}\)[/tex]:
- The fraction [tex]\(\frac{19}{21}\)[/tex] can be simplified to a decimal, which is approximately [tex]\(0.9047619047619048\)[/tex].
3. Perform the addition:
- Add the two results: [tex]\(1.8143608829626605 + 0.9047619047619048\)[/tex].
4. Simplify the addition:
- When we add these two numbers, we get approximately [tex]\(2.2527680593591826\)[/tex].
### Final Statements
By performing these calculations, we get the final results:
1. The sum [tex]\(\frac{3}{7} + 0 \approx 0.42857142857142855\)[/tex].
2. The sum [tex]\(\sqrt[6]{6} + \frac{19}{21} \approx 2.2527680593591826\)[/tex].
These values are the detailed solutions to the given expressions.
