What is the difference between square root and cube root?

A square root (²√) finds a number that, when multiplied by itself, equals the original number. A cube root (³√) finds a number that, when multiplied by itself twice, equals the original number. For example, √8 ≈ 2.828 and ³√8 = 2.

Can I calculate roots of negative numbers?

This calculator works with positive real numbers. Square roots of negative numbers require complex numbers (involving i, the imaginary unit). For complex number calculations, you would need a more advanced mathematical tool.

What are perfect squares?

Perfect squares are numbers that result from multiplying an integer by itself. Examples include 1 (1×1), 4 (2×2), 9 (3×3), 16 (4×4), 25 (5×5), etc. These have exact square roots that are integers.

How accurate are the calculations?

The calculator provides results with high precision (up to 6 decimal places). For most practical applications, this level of accuracy is sufficient. The calculations use JavaScript's built-in Math functions for maximum reliability.

What are higher roots used for?

Fourth roots (⁴√) and fifth roots (⁵√) are used in advanced mathematics, physics, and engineering. For example, fourth roots appear in some quantum mechanics calculations, while fifth roots can appear in certain geometric and algebraic applications.

How do I calculate square roots manually?

For manual calculation, you can use the long division method or Newton's method. However, for quick and accurate results, online calculators like this one are much more efficient and reliable.

Square Root Calculator

Calculate square roots and nth roots of numbers with precision and step-by-step solutions. Perfect for geometry, engineering, and mathematical applications with detailed root factorization.

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Quick Square Root Calculations

Common perfect squares for reference

Enter Number

Input the number you want to find the root of

Number

Root Type

How it works: Enter any non-negative number and select the root type. The calculator supports square root, cube root, 4th root, and 5th root with precision up to 6 decimal places.

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