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Tool Square Root Calculator

Enter any non-negative number to find its square root. The calculator shows whether the number is a perfect square, displays the value with up to 10 decimals, and visualises the result as a square with that side length.

Type a positive number, then press Calculate √. For perfect squares (1, 4, 9, 16, …) the answer will be exact.

Enter a number and press Calculate √ to see the square root.

Explained What is a Square Root?

The square root of a number is the value that, when multiplied by itself, gives the original number. It's written as √N and answers the question: "what number times itself equals N?"

Definition: √N = x means x × x = N. For example, √144 = 12 because 12 × 12 = 144.

Perfect Squares vs Non-Perfect Squares

Interesting fact: Every positive number has two square roots — one positive and one negative. The positive one is called the principal square root and is what our calculator shows by default.

Reference Perfect Squares 1–25

Click any tile to load it into the calculator instantly.

Formulas Square Root Rules & Identities

Basic Rules

Product rule:   √(a × b) = √a × √b
Quotient rule:   √(a ÷ b) = √a ÷ √b
Square of a root:   (√a)² = a
Root of a square:   √(a²) = |a|

How to Estimate Without a Calculator

  1. Find the two nearest perfect squares around your number.
  2. The root lies between their square roots.
  3. Refine the estimate using linear interpolation.
Example: Estimate √50
Nearest perfect squares: 49 = 7² and 64 = 8²
So √50 is between 7 and 8
Linear estimate: 7 + (50 − 49) / (64 − 49) = 7 + 1/15 ≈ 7.07
Actual: √50 ≈ 7.0710678…

FAQ Frequently Asked Questions

What is the square root of 144?

The square root of 144 is 12, because 12 × 12 = 144. Since 144 is a perfect square, the answer is exact.

What is a perfect square?

A perfect square is a number whose square root is a whole number. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225…

What is the square root of 2?

The square root of 2 is approximately 1.41421356. It's an irrational number, meaning it cannot be written as a simple fraction — the decimal goes on forever without repeating.

Can you find the square root of a negative number?

In real numbers, no — you can't square a real number and get a negative result. The square root of a negative number introduces the imaginary unit i, where √(−1) = i. Our calculator only accepts non-negative numbers.

How do you find the square root without a calculator?

Two main methods: prime factorization (group prime factors in pairs and pull one out of each pair) and long division (a step-by-step digit-by-digit algorithm). For estimation, find the nearest perfect squares and refine.

What does the visual diagram show?

The diagram shows a square whose area equals your input number. The side length of the square equals the square root. For example, if you entered 144, the square has area 144 and each side measures 12.

Is the square root always smaller than the number?

Yes, for any number greater than 1. For numbers between 0 and 1, the square root is actually larger (e.g., √0.25 = 0.5). For 1, √1 = 1.