What are the parts of a radical?

The horizontal bar symbol is the radical, the number underneath is the radicand, and the small number on the top left of the radical is the index.

What does simplifying a radical mean?

It means factoring out any perfect powers matching the index so that the radicand has no remaining factors that can be raised to the root index.

Can you have a negative radicand?

If the radical index is odd (like 3), the radicand can be negative (e.g., ³√(-8) = -2). If the index is even, the root is not a real number (requires complex/imaginary numbers).

Math Tool✨ New Release

Radical Calculator

Simplify radical terms (square root, cube root, or any arbitrary index) and convert radicals to rational exponent fractions with complete simplifying factors breakdown.

Interactive Radical Calculator Workspace

Live Solver

Root Index (n)

Radicand (x)

Radical Reduction Output

Simplified Radical Form6√(2)

Fractional Exponent Form(72)^(1/2)

Radical Factor Extraction Steps

Attempt to simplify ⁿ√x where index n = 2 and radicand x = 72.

Step 1: Check factors of 72 that are perfect 2-th powers.

We test integers from 8 down to 2.

Found perfect power factor: 6^2 = 36.

Factor out 6 from radical. Remaining radicand is 2.

Final expression is the simplified product: 6 × ⁿ√(2).

Mathematical Formula & Variables

Equation Modelⁿ√(x^m) = x^(m/n) | ⁿ√(a × b) = ⁿ√a × ⁿ√b

Radicals are simplified by extracting perfect nth powers from the radicand, separating them into products, and taking their root outside the radical sign.

Variable Definitions

Symbol	Description
n	The index of the radical (e.g., 2 for square root, 3 for cube root)
x	The radicand value located underneath the radical symbol
m	The power exponent inside the radical

How to Use the Radical Calculator

Input the index of the root (default is 2 for square roots).
Input the positive radicand value (number inside).
Click calculate to simplify the radical expression into mixed radical form and rational exponent form.