Precision Utility
Square Root
Calculator
Symbol
√x
Type
Perfect Squares
Enter any number to instantly calculate its square root. See whether it is a perfect square, verify the result by squaring it back, and get the cube root as a bonus. The slider lets you sweep through values from 0 to 10,000.
Enter a Number
Square Root
√144 = 12
Square Root
12
Perfect Square
Yes
Squared Back
144
Cube Root
5.2415
How the square root calculator works
Enter any non-negative number into the input field or use the slider to sweep through values from 0 to 10,000. The result updates instantly as you type or drag.
The calculator uses the standard mathematical square root function to compute the principal (positive) square root of your number. It then checks whether the result is a whole number to determine if the input is a perfect square.
You also get a verification panel that squares the result back to confirm accuracy, and a bonus cube root calculation for the same input number.
What you need to know about square roots
The square root of a number n is a value that, when multiplied by itself, gives n. It is written as √n. For example, √49 = 7 because 7 × 7 = 49.
Key concepts:
- Every positive number has two square roots: one positive and one negative. This calculator returns the principal (positive) root
- Perfect squares are numbers like 1, 4, 9, 16, 25 whose square roots are whole numbers
- The square root of 0 is 0
- Negative numbers do not have real square roots — they produce imaginary numbers
- Most square roots are irrational numbers with non-repeating, non-terminating decimals
Square roots appear throughout mathematics, science and everyday life — from the Pythagorean theorem and quadratic equations to calculating distances, standard deviations and screen diagonal measurements.
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 x 5 = 25.
What is a perfect square?
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
Can you find the square root of a negative number?
Not in the real number system. The square root of a negative number is an imaginary number. For example, the square root of -1 is written as i in mathematics.
What is the difference between a square root and a cube root?
A square root finds a value that, when multiplied by itself once, gives the original number. A cube root finds a value that, when multiplied by itself twice (three times total), gives the original number. For example, the cube root of 27 is 3 because 3 x 3 x 3 = 27.
How do you simplify a square root?
To simplify a square root, find the largest perfect square factor of the number under the radical. For example, √72 simplifies to 6√2, because 72 = 36 x 2 and the square root of 36 is 6.
Is the square root of 2 a rational number?
No. The square root of 2 is irrational, meaning it cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating: approximately 1.41421356...