An expression having radicals are in easiest forms when:
- The index cannot be decreased.
- The radicand is simplified.
- No radicals are in the denominator.
There are four rules of radicals in which will be meaningful in simplifying them.
Rule 1: (n√a)n = n√an = a
Rule 2: n√ab = n√a n√b
Rule 4: n√-a = -n√a, when n is odd.
(3√26)3 = 26
√27 = √9.3 = √9 √3 = 3√3
3√-54 = 3√(-27)(2) = (3√-27)(3√2) = -3 3√2
While a radical sign exists in the denominator, it is desirable to erase the radical. This is done through multiplying both the numerator and denominator through the radical and simplifying.