I agree that rational numbers can be written as the ratio (fraction) of two integers. Irrational numbers are non-repeating, non-terminating. 0.60719001 terminates and can be written as a fraction (although cumbersome) 60719001/100000000.
1/root (121) can be 1/11 OR - 1/11 since 121 has TWO square roots.
Regarding root (384), we can simplify 384 into 4 X 96 (not 94). The radical answer (yes this is irrational, but we are not done yet.) The greatest square factor of 384 is 64. (I kept dividing by 4 until I landed at 6) So we get the square root of 64 times the square root is 6 - or 8Xroot(6)