sqrt2P

sqrt2p is a term that may refer to the product of the square root of two and a quantity p, commonly written as √2 p or p√2. It is not a stand-alone mathematical constant; rather, its meaning depends on the value or symbol represented by p and the context in which it appears.

In geometry, if p denotes a side length, p√2 is the length of the diagonal of a square with side p, since the diagonal d satisfies d^2 = p^2 + p^2 = 2p^2, giving d = p√2. In algebra and physics, √2 p appears as a scaling factor multiplying p in equations or models, used to express quantities that grow or scale by the factor √2.

Properties of √2 are relevant here: the number √2 is irrational, so for any nonzero rational p, the product p√2 is irrational. If p is irrational, the product can be either rational or irrational depending on p. The expression inherits the usual arithmetic conventions: √2 p means the same as p√2, and both are real numbers whenever p is real.

Usage and notes: because sqrt2p is not a fixed mathematical object, it is context-dependent and should be read from the surrounding notation. In programming or calculators, it is often represented as p * sqrt(2).