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Simplifying Radical Expressions Square Roots Calculator

Reviewed by Calculator Editorial Team

Radical expressions involve square roots and other roots. Simplifying them makes them easier to work with in equations and calculations. This guide explains how to simplify radical expressions using square roots, including step-by-step methods and practical examples.

What are radical expressions?

A radical expression is a mathematical expression that contains a radical symbol (√) and a radicand (the number under the radical). The most common type is the square root (√), but other roots like cube roots (∛) also exist. Radical expressions can be simplified by removing perfect square factors from the radicand.

√(a·b) = √a · √b √(a/b) = √a / √b

Simplifying radical expressions involves breaking down the radicand into its prime factors and then separating the perfect squares from the remaining factors.

How to simplify square roots

To simplify a square root, follow these steps:

  1. Factor the radicand into perfect squares and other factors.
  2. Separate the square root of the perfect square from the other factors.
  3. Simplify the square root of the perfect square.
  4. Combine the simplified terms.

Example: Simplify √(72)

  1. Factor 72: 72 = 36 × 2
  2. √(72) = √(36 × 2) = √36 × √2
  3. √36 = 6
  4. √(72) = 6√2

This process works for any square root expression. The calculator automates these steps for you.

Using the calculator

The calculator simplifies square roots and radical expressions. Enter the radicand (the number under the square root) and click "Calculate" to get the simplified form.

For example, entering "72" will return "6√2". The calculator also shows the step-by-step simplification process.

Examples

Here are some examples of simplified radical expressions:

  • √(27) = 3√3
  • √(50) = 5√2
  • √(108) = 6√3
  • √(192) = 8√3

These examples demonstrate how to simplify square roots by factoring and separating perfect squares.

FAQ

What is a radical expression?

A radical expression is a mathematical expression that contains a radical symbol (√) and a radicand (the number under the radical). The most common type is the square root.

How do I simplify a square root?

To simplify a square root, factor the radicand into perfect squares and other factors, then separate the square root of the perfect square from the other factors.

Can the calculator simplify cube roots?

This calculator focuses on square roots. For cube roots, you would need a different tool or method.