Square Root Simplifier with Steps

Simplify square roots (radicals) step by step. Find perfect square factors and see the complete simplification process.

Enter a positive integer (e.g., 72, 50, 18)
Optional number outside the radical (e.g., 3√5)

Simplified Result

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Numerical Value

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Approximate decimal value

Quick Reference

√4 = 22
√8 = 2√22.828
√12 = 2√33.464
√18 = 3√24.243
√20 = 2√54.472

Step-by-Step Solution

Enter a number and click "Simplify" to see the step-by-step simplification process.

Perfect Squares Reference

Number Square Root Number Square Root
11648
42819
9310010
16412111
25514412
36616913
49719614

How to Simplify Square Roots

  • Step 1: Find the largest perfect square factor of the number
  • Step 2: Write the number as a product of that perfect square and another factor
  • Step 3: Take the square root of the perfect square
  • Step 4: Leave the other factor under the radical

Example: Simplify √72

  • √72 = √(36 × 2)
  • √72 = √36 × √2
  • √72 = 6 × √2
  • √72 = 6√2

Common Perfect Squares

  • 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196
  • Look for the largest perfect square that divides evenly
  • Prime factorization can also help find factors

Square Root Simplifier: Learn to Simplify Radicals Step by Step

What is a Square Root? The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3 × 3 = 9. Simplifying square roots involves removing perfect square factors from under the radical sign.

How to Simplify Square Roots

Step 1: Find the largest perfect square that divides evenly into your number.

Step 2: Rewrite the number as the product of that perfect square and another factor.

Step 3: Take the square root of the perfect square (this becomes the coefficient).

Step 4: Leave the other factor under the square root symbol.

Example Simplification

Simplify √72

Simplifying with Coefficients

When you have a coefficient outside the radical (like 3√72), simplify the radical first, then multiply:

Math Tip: When simplifying square roots, always look for the largest perfect square factor. Using prime factorization can help: break the number into prime factors, then pair them up. Each pair becomes a whole number outside the radical.