In precalculus, what is the difference between a principal value and an exact value?

Answer 1

While not related, here's an explanation of each...

Exact typically means to leave as a root or fraction, especially in the cases where the decimal would have to be rounded or approximated.

EX: √2 would be left as √2, not as 1.414...

√9 could be written as 3

22/7 would be left as 22/7

A principal value is typically the smallest value that meets the criteria.

EX: arcsin(1)=π/2 radians or 90° (principal values), where other values would be 5π/2 rads, 9π/2 rads, etc or 450°, 810°, etc.