# Radical (Math)

## The Effect Of N And R On P

Both the radicand *R* and the order of the root *n* have an effect on the root(s) *P*. For example, because a **negative** number multiplied by a negative number is a **positive number**, the even roots (*n* = 2, 4, 6, 8...) of a positive number are both negative and positive: √9 = ±3, &NA; = ±2.

Because the root *P* of &NA; must be multiplied an odd number of times to generate the radicand *R*, it should be clear that the odd roots (*n* = 3, 5, 7, 9...) of a positive number are positive, and the odd roots of a negative number are negative. For example, &NA; = 2 (2^{3} = 2 × 2 × 2 = 4 × 2 = 8), but &NA; = −2 (−2^{3} = −2 × −2 × −2 = 4 × −2 = 8).

Taking an even root of a negative number is a trickier business altogether. As discussed above, the product of an even number of negative values is a positive number. The even root of a negative number is imaginary. That is, we define the imaginary unit *i* = √−1 or 2 *i* = −1. Then √−9 = √9 × √−1 = ±3*i*. The imaginary unit is a very useful concept in certain types of **calculus** and complex analysis.

## Additional topics

Science EncyclopediaScience & Philosophy: *Quantum electronics* to *Reasoning*Radical (Math) - Types of radical operations, The effect of n and R on P, simplification of radicals Operations