Radicand

Radicand is the quantity inside a radical symbol in mathematics. In the square root example sqrt(9), the radicand is 9. For a general nth root, written as the nth root of a or sqrt[n]{a}, the radicand is a.

The radicand can be any number or expression: a constant, a variable, a polynomial, or a more complex algebraic expression. The value of the radical depends on both the radicand and the index of the root.

In real-number arithmetic, the index influences the permissible radicands. If the index is even, the radicand must be nonnegative to yield a real number; a negative radicand under an even root has no real value. If the index is odd, the root exists for every real radicand and gives a real result. In complex numbers, roots of negative radicands are defined but involve imaginary numbers and multiple branches.

Radicands are often simplified in the process of simplifying radicals. For example, sqrt(50) can be rewritten as 5 sqrt(2) by factoring 50 into a product of a perfect square and another factor. The radicand itself is not changed in value; rather, factors are extracted or combined to produce a simpler form.

Origin and usage: the term radicand derives from the concept of the root, reflecting the quantity that is being "rooted" by the radical symbol. The concept is fundamental in algebra, calculus, and various applications where expressions are manipulated under radical operators.