radicand

The radicand is the quantity sitting under the radical sign — the number or expression you are taking the root of. In sqrt(50), the radicand is 50; in the cube root of (x + 1), the radicand is x + 1.

Knowing the radicand matters for two reasons. First, simplifying a radical means factoring the radicand to find perfect-power pieces you can pull out: sqrt(50) = sqrt(25 × 2) splits off the perfect square 25. Second, the radicand controls whether the root is even defined among real numbers.

For an even root such as a square root, the radicand cannot be negative if you want a real answer, since no real number squares to a negative. This is why, when a variable appears in the radicand, you often state a domain restriction — for sqrt(x) to be real, you need x ≥ 0. Odd roots place no such restriction on the radicand.