Roots and Powers

√(49) is 7, because 7 squared is 49. So is -7 squared, but the root sign always means the non-negative one. In general √(a) is the non-negative number whose square is a. No real number squares to a negative, so √(-9) is not a real number.

A cube root undoes a cube: cbrt(8) is 2, because 2 cubed is 8. A cube keeps the sign of what was cubed, so negatives are allowed here: -2 cubed is -8, which makes cbrt(-8) equal to -2.

Roots split over a product. √(4 × 9) is √(36), which is 6, and √(4) × √(9) is 2 times 3, also 6. The rule is √(ab) = √(a)√(b) for a and b not negative. It is how a root gets simpler: √(28) = √(4) × √(7), which is 2√(7). A root with no square factor left inside is in simplest radical form.