Square Root Calculator

Enter a number to find its square root, cube root, and check if it is a perfect square or perfect cube.

Square Root (√)

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Cube Root (∛)

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Perfect Square?

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Perfect Cube?

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Nearby Perfect Squares

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Nearby Perfect Cubes

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Understanding Roots

What is a Square Root?

The square root of a number is a value that, when squared, equals the original. Written as √n.

Examples: √4 = 2, √9 = 3, √2 ≈ 1.414

Cube Roots

The cube root of a number is a value that, when cubed, equals the original. Written as √[3]n or n^(1/3).

Examples: √[3]8 = 2, √[3]27 = 3, √[3]64 = 4

Properties of Square Roots

  • √(a × b) = √a × √b
  • √(a / b) = √a / √b
  • (√a)² = a
  • √(a²) = |a| (absolute value)

Estimation Without a Calculator

To estimate a square root, find the two perfect squares it falls between:

  • √50: Between √49 = 7 and √64 = 8, closer to 7 → ≈ 7.07
  • √20: Between √16 = 4 and √25 = 5, closer to 4.5 → ≈ 4.47

Common Perfect Squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Common Perfect Cubes

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Frequently Asked Questions

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. Every positive number has two square roots: a positive one and a negative one (e.g., both 5 and -5 are square roots of 25). By convention, the "square root" symbol (√) refers to the positive root.
Can negative numbers have square roots?
In the real number system, negative numbers do not have square roots because no real number multiplied by itself gives a negative result. However, in the complex number system, the square root of -1 is defined as "i" (the imaginary unit), so √(-9) = 3i. This calculator works with real numbers only.
What are perfect squares?
A perfect square is a number that is the product of an integer multiplied by itself. The first 15 perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Their square roots are the whole numbers 1 through 15.
What is the difference between square root and cube root?
A square root (√) finds a number that, multiplied by itself twice, gives the original number (e.g., √27 is not a whole number, but √25 = 5). A cube root (∛) finds a number that, multiplied by itself three times, gives the original number (e.g., ∛27 = 3 because 3 × 3 × 3 = 27). Cube roots can also be taken of negative numbers.

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