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Square Root Calculator

Calculate the square root of any non-negative number. Get detailed results including the principal root, simplified radical form, and perfect square detection.

Square Root Calculator

Calculate the square root of any non-negative number. Get detailed results including the principal root, simplified radical form, and perfect square detection.

Max 14 digits
decimal places

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, equals the original number. Every positive number has two square roots: a positive one and a negative one. However, the radical symbol (√) specifically refers to the principal square root, which is the non-negative value. For example, while both 3 and -3 are square roots of 9, we write √9 = 3.

x=y    y2=x where y0\sqrt{x} = y \implies y^2 = x \text{ where } y \ge 0

Examples

4=2\sqrt{4} = 2(perfect square)
9=3\sqrt{9} = 3(perfect square)
21.414\sqrt{2} \approx 1.414(irrational)
12=23\sqrt{12} = 2\sqrt{3}(simplified)

Tips for Using the Calculator

  • Enter any non-negative number (integers or decimals).
  • Perfect squares (e.g., 1, 4, 9, 16) result in whole numbers.
  • Non-perfect squares result in irrational numbers (infinite non-repeating decimals).
  • Adjust the precision (1-20 decimal places) to control the accuracy of the result.
  • Use the 'Show ± roots' option to see both positive and negative solutions.