Without using a calculator how do you determine whether a RADICAL
represents a rational or an irrational number? Use examples to explain.
Prime factor the integer under the radical
Call the index of the radical, n
If n does not evenly divide every exponent in the prime factorization, then we have an irrational result
2√ 16 = 2√2^4 2 divides 4 evenly,,,so we have a rational answer because √16 = 4
3√ 32 = 3√ 2^5 since 3 does not evenly divide 5, we have an irrational answer = 23√2^2 = 23√4