# Square Root Calculator

Calculate the square root of any number instantly. Check if a number is a perfect square and see the simplified radical form. Free online square root tool.

## What this calculates

Find the square root of any non-negative number with this free online calculator. It computes the principal square root, tells you whether the number is a perfect square, and provides the simplified radical form for integer inputs.

## Inputs

- **Number** — min 0 — Enter a non-negative number to find its square root.

## Outputs

- **Square Root** — The principal (positive) square root of the number.
- **Perfect Square?** — formatted as text — Whether the input is a perfect square.
- **Number Squared** — The input number multiplied by itself (for reference).
- **Simplified Radical** — formatted as text — The square root in simplified radical form (for integers).

## Details

The square root of a number x is a value y such that y x y = x. For example, the square root of 25 is 5, because 5 x 5 = 25. The symbol for square root is the radical sign.

Key Concepts

- Principal Square Root: Every positive number has two square roots (one positive, one negative), but the principal square root is the positive one. For example, sqrt(9) = 3, not -3.

- Perfect Squares: A number is a perfect square if its square root is an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

- Simplified Radical Form: A radical expression is simplified when no perfect square factor remains under the radical sign. For example, sqrt(72) = sqrt(36 x 2) = 6 x sqrt(2).

- Imaginary Numbers: The square root of a negative number is not a real number. In the complex number system, sqrt(-1) is defined as i (the imaginary unit).

Square roots appear in geometry (Pythagorean theorem, distance formula), physics (energy equations, wave mechanics), statistics (standard deviation), and many other fields.

## Frequently Asked Questions

**Q: What is a square root?**

A: The square root of a number x is a value that, when multiplied by itself, gives x. For example, the square root of 49 is 7 because 7 x 7 = 49. Every positive number has two square roots: a positive and a negative one.

**Q: What is a perfect square?**

A: A perfect square is an integer that is the square of another integer. For example, 36 is a perfect square because 6 x 6 = 36. The first 15 perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

**Q: How do I simplify a square root?**

A: Factor the number under the radical into a product where one factor is the largest perfect square. Then take the square root of the perfect square factor. For example, sqrt(200) = sqrt(100 x 2) = 10 x sqrt(2). The key is finding the largest perfect square factor.

**Q: Can I take the square root of a negative number?**

A: Not in the real number system. In the complex number system, the square root of a negative number uses the imaginary unit i, where i = sqrt(-1). For example, sqrt(-16) = 4i. This calculator handles real numbers only.

**Q: What is the square root of 2?**

A: The square root of 2 is approximately 1.41421356. It is an irrational number, meaning its decimal expansion goes on forever without repeating. It is one of the most important irrational numbers and appears frequently in geometry, especially in relation to 45-45-90 triangles.

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Source: https://vastcalc.com/calculators/math/square-root
Category: Math
Last updated: 2026-04-21