Math & Algebra Tool

Square Root Calculator

Find square roots and simplify radicals with steps.

Σ The Formula

√x = x^(1/2)

Real World Examples

Perfect Square
√16 = 4
Irrational
√2 ≈ 1.414
Simplify Radical
√50 = √(25×2) = 5√2
Large Number
√144 = 12

# About This Calculator

The Square Root of a number is a value that, when multiplied by itself, gives the original number. For example, 4 is the square root of 16 because 4 × 4 = 16. It is indicated by the radical symbol (√).

Square roots are fundamental in geometry (Pythagorean theorem, distances), algebra (solving quadratic equations), and physics. Most numbers aren't perfect squares, meaning their square root is an irrational number (a non-repeating decimal that goes on forever).

This tool simplifies radicals to their exact form (like turning √12 into 2√3) and provides the decimal approximation. Simplifying radicals is crucial for exact answers in math class.

Use this to solve right triangles, check homework, or find the side length of a square given its area.

How To Use

  1. Enter a non-negative number.
  2. Click Calculate.
  3. See both the exact simplified radical and the decimal value.

Frequently Asked Questions

What is a perfect square?+

A number whose square root is a whole integer. Examples: 1, 4, 9, 16, 25, 36. 10 is not a perfect square because √10 ≈ 3.16.

Why can't I find the square root of a negative number?+

In real numbers, no number multiplied by itself gives a negative result (positive × positive = positive, negative × negative = positive). You need complex numbers (imaginary unit i) for that.

How do you simplify a radical like √12?+

Find the largest perfect square factor. 12 = 4 × 3. Since √4 = 2, then √12 = √(4×3) = 2√3.

Is √x always positive?+

The principal square root (√) refers to the non-negative root. While (-4)² = 16, √16 is defined as just 4, not -4.

How is square root related to exponents?+

Square root is the same as raising to the power of 1/2. √x = x^(1/2). Cube root is power of 1/3.

Is Square Root Calculator free to use?+

Yes, Square Root Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

The Square Root of a number is a value that, when multiplied by itself, gives the original number. For example, 4 is the square root of 16 because 4 × 4 = 16. It is indicated by the radical symbol (√).

Square roots are fundamental in geometry (Pythagorean theorem, distances), algebra (solving quadratic equations), and physics. Most numbers aren't perfect squares, meaning their square root is an irrational number (a non-repeating decimal that goes on forever).

This tool simplifies radicals to their exact form (like turning √12 into 2√3) and provides the decimal approximation. Simplifying radicals is crucial for exact answers in math class.

Use this to solve right triangles, check homework, or find the side length of a square given its area.

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