Radical — Definition, Symbol & Examples

Radical

The Square root symbol (radical sign): √ symbol, which is used to indicate square roots or nth roots.

See also

Key Formula

\sqrt[n]{a}

Where:

$\sqrt{\phantom{x}}$ = The radical symbol
$n$ = The index, indicating which root to take (2 for square root, 3 for cube root, etc.)
$a$ = The radicand — the number or expression inside the radical

Worked Example

Problem: Simplify √49 and ∛27.

Step 1: For √49, find the number that, when multiplied by itself, gives 49.

\sqrt{49} = 7 \quad \text{because } 7 \times 7 = 49

Step 2: For ∛27, find the number that, when multiplied by itself three times, gives 27.

\sqrt[3]{27} = 3 \quad \text{because } 3 \times 3 \times 3 = 27

Answer: √49 = 7 and ∛27 = 3.

Why It Matters

Radicals appear throughout algebra, geometry, and science whenever you need to reverse an exponent. For instance, the Pythagorean theorem often requires a square root to find a missing side length, and the quadratic formula contains a radical. Understanding radical notation is essential for working with fractional exponents, since

\sqrt[n]{a} = a^{1/n}

Common Mistakes

Mistake: Confusing the radicand with the index. For example, reading ∛8 and thinking 3 is the radicand.

Correction: The radicand is the value inside the radical (8 in this case). The index is the small number outside and above the radical symbol (3), indicating which root to take.

Related Terms

Radical Rules — Properties for simplifying radical expressions
Square Root — The most common type of radical (index 2)
Exponent — Radicals are the inverse of exponents
Radicand — The expression inside the radical symbol