Select all numbers that are irrational. 1049−−√ 3.14 π 0.5

Please, separate your numbers with commas, or put each one on its own line.
I do not know what you mean by 1049--    or by   --√ 3.14.  "--" does not belong in such a list.

1049 = 1049/1 is rational.

√ 3.14 = sqrt(pi) is irrational; can't express it as the ratio of two integers.

pi is irrational (same reason as above)

0.5 is rational; it's the ratio of integers 1 and 2:  1/2