To determine the greatest prime number less than [tex]\(\sqrt{189}\)[/tex], follow these steps:
1. Calculate [tex]\(\sqrt{189}\)[/tex]:
- [tex]\(\sqrt{189}\)[/tex] is approximately 13.74772708486752.
2. Identify prime numbers less than 13.74772708486752:
- The prime numbers less than 13.74772708486752 are 2, 3, 5, 7, 11, and 13.
3. Determine the greatest prime number from the list:
- Among the prime numbers less than 13.74772708486752, 13 is the greatest.
Thus, the greatest prime number less than [tex]\(\sqrt{189}\)[/tex] is:
a) 13
