Radicand

High School

Definition

A number under the radical symbol (sometimes known as the square root symbol). It is the number that is having its root taken. It could be a square root, but you likely will encounter cube roots and more. A subscript outside the radical sign will allow you to identify which root you're dealing with.

Worked examples

\(\sqrt{25}\)

The radicand is 25 — the number whose square root we're finding.

\(\sqrt[3]{-8}\)

The radicand is -8, and the subscript 3 tells us it's a cube root.

\(\sqrt{x^2 + 4x + 4}\)

The entire expression \(x^2 + 4x + 4\) is the radicand under the square root.

Common mistakes

\(\sqrt[3]{27}\) → the radicand is 3 → \(\sqrt[3]{27}\) → the radicand is 27 The subscript 3 is the index (type of root), not the radicand. The radicand is always the number inside.
\(5\sqrt{7}\) → the radicand is \(5 \cdot 7\) → \(5\sqrt{7}\) → the radicand is 7 Only the number under the radical symbol is the radicand; the coefficient 5 sits outside.

Where you'll use it next

You'll work with radicands when simplifying radicals, solving radical equations, rationalizing denominators, and later in calculus when differentiating and integrating expressions containing roots.

Found in 1 StudyPug lesson

Simplifying Radicals: A Comprehensive Guide

Precalculus

Unlock the secrets of simplifying radicals with our step-by-step approach. Learn to tackle square roots, cube roots, and complex expressions with confidence and precision.

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