Square Root Calculator Simplify Radicals
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Reviewed by Calculator Editorial Team
This square root calculator helps you simplify radicals by breaking down complex square roots into simpler forms. Whether you're dealing with √a/b, √(a±b), or other radical expressions, this tool provides step-by-step guidance to simplify them efficiently.
How to Use This Calculator
Enter the radical expression you want to simplify in the input field. The calculator will analyze the expression and provide the simplified form. You can also use the calculator to verify your manual simplification work.
For best results, enter the radical in the form √(numerator/denominator) or √(a±b). The calculator handles both rational and irrational numbers.
Simplifying Radicals
Simplifying radicals involves breaking down the square root into its simplest form. Here's how to do it:
- Factor the number under the square root into perfect squares and other factors.
- Separate the square root into two parts: one with the perfect square and another with the remaining factors.
- Simplify the square root of the perfect square.
For example, to simplify √36:
- Factor 36 into 6 × 6 (both perfect squares).
- √36 = √(6 × 6) = √6 × √6 = 6.
For more complex expressions like √(a/b), follow these steps:
- Simplify the numerator and denominator separately.
- Combine the simplified forms under a single square root.
- If possible, rationalize the denominator.
Examples
Here are some examples of simplified radicals:
| Original Expression | Simplified Form |
|---|---|
| √36 | 6 |
| √(18/2) | 3 |
| √(50/2) | 5√2 |
| √(a² + 2ab + b²) | a + b |
These examples demonstrate how to simplify different types of radical expressions.
FAQ
- What is the difference between a radical and a square root?
- A radical is a mathematical expression involving a root, such as a square root, cube root, etc. A square root is a specific type of radical that involves the second root of a number.
- How do I simplify a radical with a denominator?
- To simplify a radical with a denominator, rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
- Can I simplify radicals with variables?
- Yes, you can simplify radicals with variables by factoring out perfect square factors from the variable part of the expression.
- What is the difference between √(a±b) and √a ± √b?
- √(a±b) represents a single square root of the sum or difference of a and b, while √a ± √b represents the sum or difference of two separate square roots.
About this calculator
Updated June 25, 2026. Formulas, assumptions, and limitations are shown directly on this page.
Formula and Assumptions
The calculator uses standard radical simplification rules. For expressions like √(a/b), it simplifies the numerator and denominator separately and combines the results.
Assumptions: All inputs are real numbers. Complex numbers are not supported.