Every Toolkit

Square Root Calculator

Calculate square roots, cube roots, and squares instantly. Perfect for math homework, engineering, and scientific calculations.

Calculate Roots

Enter a number to calculate its square root, cube root, and square

📊 Perfect Squares Reference

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

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About Square Root Calculator

Our Square Root Calculator helps you quickly calculate square roots, cube roots, and squares of any number. Perfect for students, engineers, scientists, and anyone working with mathematical calculations.

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 × 5 = 25. The square root symbol is √.

Features

  • Calculate square roots (√x)
  • Calculate cube roots (∛x)
  • Calculate squares (x²)
  • High precision results (10 decimal places)
  • Perfect square detection
  • Copy results to clipboard
  • Perfect squares reference table

Common Use Cases

  • Mathematics: Solving equations, geometry problems
  • Physics: Calculating velocity, acceleration
  • Engineering: Structural calculations, design
  • Statistics: Standard deviation calculations
  • Finance: Compound interest, growth rates
  • Computer Science: Algorithm complexity

Perfect Squares

A perfect square is a number that is the square of an integer. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. Our calculator automatically detects if your number is a perfect square.

Square Root Properties

  • √(a × b) = √a × √b
  • √(a / b) = √a / √b
  • √a² = |a|
  • (√a)² = a
  • √1 = 1
  • √0 = 0

Cube Roots

A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27. The cube root symbol is ∛.

How to Use

  1. Enter any positive number in the input field
  2. Click "Calculate" or press Enter
  3. View the square root, cube root, and square
  4. Click the copy icon to copy any result
  5. Check if the number is a perfect square

Examples

  • √16 = 4 (perfect square)
  • √2 = 1.414213562... (irrational number)
  • √100 = 10 (perfect square)
  • √50 = 7.071067812...
  • ∛8 = 2 (perfect cube)
  • ∛27 = 3 (perfect cube)

Tips

  • Use decimal numbers for precise calculations
  • Results show 10 decimal places for accuracy
  • Perfect squares have integer square roots
  • Negative numbers don't have real square roots
  • The square root of 1 is always 1

Applications in Real Life

  • Construction: Calculating diagonal distances
  • Navigation: Distance calculations using Pythagorean theorem
  • Finance: Calculating compound annual growth rate
  • Science: Standard deviation in statistics
  • Gaming: Distance calculations in 2D/3D space