Sqrtpn

Sqrtpn is ambiguous and not a standard mathematical object. It appears in various contexts as a compact notation, and its meaning depends on the field or author.

One interpretation treats sqrtpn as the principal square root of the product p n, written as sqrt(p n). This interpretation regards p and n as positive real numbers, and the value is obtained by applying the square root to their product. In problems involving scaling, areas, or length factors, sqrt(p n) may describe a combined scaling by p and n.

A different use defines sqrtpn as the square root of the nth prime, written sqrt(p_n), where p_n denotes the nth prime (p_1 = 2, p_2 = 3, p_3 = 5, ...). In this sense, sqrt(p_n) is irrational for every n, since p_n is prime. As p_n increases with n, sqrt(p_n) is strictly increasing as well. For example, sqrt(p_1) = sqrt(2) ≈ 1.4142 and sqrt(p_6) = sqrt(13) ≈ 3.6055.

Because sqrtpn has no single standard meaning, readers must rely on the surrounding definitions. The two interpretations above illustrate typical usage: a straightforward arithmetic square root of a product, or the square root of a prime indexed by n.

See also: square root, prime numbers, p_n.