Radicals – The Root Symbol Explained

A radical is the general name for any root expression, written with the √ symbol. So far this section has covered the two most common radicals – square roots (√n) and cube roots (∛n) – but the same symbol extends to any root at all: a small number called the index, written just before the radical sign, shows exactly which root is meant. Without a visible index, a radical is always assumed to mean a square root.

The Parts of a Radical

In ⁿ√x, n is the index (which root), and x is the radicand (the number under the root symbol). When n is omitted, it means a square root (n = 2).

In the radical ⁴√81, identify the index and the radicand.

The index is 4 (a fourth root), and the radicand is 81 (the number under the root).

Evaluating a Radical

Evaluate ⁴√16.

2 × 2 × 2 × 2 = 16, so ⁴√16 = 2.

Real-Life Application

Engineering: some formulas require fourth or higher roots.
Statistics: certain calculations use nth roots to find geometric means.
Computer graphics: some scaling algorithms use higher-order roots.

Key Takeaways

A radical ⁿ√x has an index n (which root) and a radicand x (the number under the root).
A radical with no visible index is assumed to be a square root.
Simplifying radicals, covered next, shows how to reduce a radical to its cleanest form.

Practice: Radicals

Identify the Parts of a Radical