Square Root Calculator
Calculate the square root of any non-negative number. Detects perfect squares and shows the simplified radical form for non-perfect ones.
Find a square root
Enter any non-negative number.
sqrt(144) =
12
144 is a perfect square.
Frequently Asked Questions about the Square Root Calculator
What is a square root?
The square root of a number x is the value that, when multiplied by itself, equals x. The square root of 25 is 5 because 5 x 5 = 25.
Can I take the square root of a negative number?
Not with real numbers. The square root of a negative number is imaginary, denoted by i (where i x i = -1). This calculator only handles real, non-negative inputs.
What is a perfect square?
A perfect square is an integer whose square root is also an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
What does the simplified radical form mean?
For non-perfect squares, you can pull the largest perfect-square factor out of the radical. For example, sqrt(72) = sqrt(36 x 2) = 6 sqrt(2). It is the exact value in its simplest form.
How is square root calculated?
Computers use efficient iterative methods such as Newton's method. By hand, you can guess and refine, or use prime factorization to identify perfect-square factors.
What is the square root of 2?
Approximately 1.41421356. It is irrational, meaning its decimal expansion never repeats or terminates.