Sure, let's convert each of the given Roman numerals to their corresponding Hindu-Arabic numbers step-by-step.
### Conversion steps:
1. VIII
- 'VIII' stands for 8.
2. XL
- 'XL' stands for 40.
3. XV
- 'XV' stands for 15.
4. XVI
- 'XVI' stands for 16.
5. XXVII
- 'XXVII' stands for 27.
6. XXX [tex]\(\sqrt{III}\)[/tex]
- 'XXX' typically stands for 30, and '[tex]\(\sqrt{III}\)[/tex]' would imply taking the square root of 'III' which is 3. The square root of 3 ([tex]\(\sqrt{III}\)[/tex]) is approximately 1.732, but this Roman numeral is treated as 'XXXIII' which stands for 33.
7. XXXIV
- 'XXXIV' stands for 34.
8. XX
- 'XX' stands for 20.
9. XVII
- 'XVII' stands for 17.
10. XIX
- 'XIX' stands for 19.
### Final Hindu-Arabic Numbers:
a. [tex]\( VIII \)[/tex] = 8
b. [tex]\( XL \)[/tex] = 40
c. [tex]\( XV \)[/tex] = 15
d. [tex]\( XVI \)[/tex] = 16
e. [tex]\( XXVII \)[/tex] = 27
f. [tex]\( XXX \sqrt{III} \)[/tex] = 33
g. [tex]\( XXXIV \)[/tex] = 34
h. [tex]\( XX \)[/tex] = 20
i. [tex]\( XVII \)[/tex] = 17
j. [tex]\( XIX \)[/tex] = 19
Thus, the Hindu-Arabic numbers corresponding to the given Roman numerals are [tex]\(8, 40, 15, 16, 27, 33, 34, 20, 17\)[/tex], and [tex]\(19\)[/tex].
