cbrt5

cbrt5 denotes the real cube root of 5, commonly written as ∛5 or 5^(1/3). It is the real number x such that x^3 = 5. In decimal form, ∛5 is approximately 1.709975947. It is an irrational number and an algebraic number of degree 3, since it is a root of the polynomial x^3 − 5 with rational coefficients. The other two cube roots of 5 are complex: ∛5 · ω and ∛5 · ω^2, where ω = e^(2πi/3) is a primitive cube root of unity; these are complex conjugates.

As a mathematical object, ∛5 is the principal real root, and more generally 5^(1/3) denotes the same value in exponent form. It is used whenever a quantity equals the cube of something that equals 5, such as finding a side length given a cube’s volume of 5 cubic units. In algebra, such cube roots appear in solving cubic equations and in expressions produced by Cardano’s method. Although simple in form, ∛5 is not reducible to a rational number or a combination of square roots; it remains an independent cubic radical.