100% Client-Side • Principal Root Solver • Perfect Squares & Radical Reductions

Square Root Calculator

Calculate the exact principal square root of any non-negative integer, decimal, or fraction.

1Enter Number

√144 = 12

Number (x ≥ 0)

√x

Common Perfect Squares:

Example Math Problems

Decimal Precision4 Decimals

Principal Square RootPerfect Square ★

√144 = 12

Input Number: 144Check: 12 × 12 = 144Power: 144^(1/2) = 12

√Mathematical Properties & Exact Forms

Reverse Verification (Root Squared)12 × 12 = 144

Exponential Form144^(1/2) = 12

Number TypePerfect Square (Rational)

✓Step-by-Step Square Root Evaluation

1. Identify the input number: x = 144.

2. Find a number whose square equals 144: 12² = 12 × 12 = 144.

3. Since 144 is a perfect square, its square root is exactly 12.

4. Conclusion: √144 = 12.

Square Root Computation Statement

Summary statement and numerical radical properties.

The square root of 144 is exactly 12 because 12 × 12 = 144. (144 is a perfect square).

About Square Root Calculator

Square Root & Radical Calculator. Calculate principal square roots (√x), radical simplifications, and evaluate perfect and non-perfect squares. ZechKit provides this tool completely free and online, optimized for instant, accurate computations directly inside your web browser.

In-Depth Guide & Usage

A Square Root Calculator finds the non-negative principal value (y) that, when multiplied by itself, produces the original number (x): y = √x such that y² = x.

Perfect vs. Non-Perfect Squares: Perfect squares (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...) yield whole integer roots. Non-perfect squares yield infinite, non-repeating irrational decimals (e.g. √2 ≈ 1.41421356...).

Radical Properties: Product Property: √(a × b) = √a × √b. Quotient Property: √(a / b) = √a / √b.

Geometric Significance: The square root represents the side length of a square with a known area, and is central to the Pythagorean theorem (c = √(a² + b²)) and distance formulas.

Technical Specifications

CategoryMath

Target ValueSquare Root

Inputs Required (1)

Number (number)

Frequently Asked Questions

The principal square root is the non-negative square root of a positive real number (e.g., √25 = 5, even though (−5)² also equals 25).

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