Simplify Radicals Calculator

Simplified Form
Coefficient Outside
Inside Radical
Explanation

How It Works

This simplify radicals calculator uses established formulas to provide accurate results.

The basic rule:

  • √(a·b) = √a · √b
  • Find largest perfect square factor
  • √n = c√r where c² · r = n

Results are estimates. Consult a professional for critical decisions.

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Frequently Asked Questions

How do I simplify a square root?

Find the largest perfect square that divides the radicand. Factor it out, take its square root, and leave the rest under the radical. For example, √72 = √(36·2) = 6√2.

What is a perfect square?

A perfect square is a number that is the square of an integer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. When simplifying, look for the largest perfect square factor.

When is a radical fully simplified?

A radical is fully simplified when no perfect square factor (other than 1) remains under the radical sign. For example, √12 is not simplified (contains factor 4), but 2√3 is.

Can you simplify √2?

No. Since 2 has no perfect square factors other than 1, √2 is already in simplest radical form. It is an irrational number approximately equal to 1.414.