Simplify Radicals Calculator | Square Root Simplifier

Simplify Radicals

This calculator helps you simplify radical expressions by finding the largest perfect square factor of the radicand. Enter any positive integer to get its simplest radical form.

Radicand (Positive Integer)

Enter the number under the square root symbol (e.g., 72)

Please enter a positive integer for the radicand.

How it works

This calculator helps you simplify radical expressions by finding the largest perfect square factor of the radicand. Enter any positive integer to get its simplest radical form.

The Formula

To simplify a radical (square root), find the largest perfect square factor of the radicand. Then, take the square root of that factor and leave the remaining factor inside the radical.

Example: √A = √(B² * C) = B√C

Worked Example

Example: Simplify √72
To simplify √72: 1. Find the prime factors of 72: 2 × 2 × 2 × 3 × 3. 2. Group pairs of identical factors: (2 × 2) × (3 × 3) × 2. 3. For each pair, one factor comes out of the radical: 2 × 3 = 6. 4. The remaining factor(s) stay inside: 2. 5. So, √72 simplifies to 6√2.

Tips, Assumptions & Limitations

Only positive integers can be simplified using this tool.
Remember that a perfect square is a number that can be expressed as the product of an integer by itself (e.g., 4, 9, 16).
The calculator will show you the simplified form, like A√B.

FAQ

In mathematics, a radical is an expression that involves a root, most commonly a square root (√). It's used to denote the root of a number.

Simplifying radicals makes mathematical expressions easier to work with, compare, and understand. It's a standard practice in algebra to present radical expressions in their simplest form.

No, this specific calculator is designed to simplify square roots only. For cube roots or other higher roots, the process involves looking for groups of three (or more) identical factors.

Simplifying radicals with variables follows a similar principle: look for pairs of identical variables (e.g., x²). For example, √(x³y²) simplifies to xy√x. This calculator focuses on numerical radicands.