Math
Square Root Calculator
Calculate the square root, cube root, or any nth root of a number instantly. Supports negative roots with imaginary results.
Enter a number above
Advertisement
Root Formulas
√x = x^(1/2)
∛x = x^(1/3)
ⁿ√x = x^(1/n)
The square root undoes squaring; the cube root undoes cubing; the nth root undoes raising to the nth power.
How to Use This Calculator
Select the root type — square root (√), cube root (∛), or custom nth root (ⁿ√). Enter the number and the calculator returns the result with a formula notation and a verification check.
For even-indexed roots of negative numbers, an error is shown because those results are imaginary.
Frequently asked questions
What is a square root?
The square root of a number x is the value that, when multiplied by itself, equals x. For example, the square root of 25 is 5 because 5 × 5 = 25.
What are perfect squares?
Perfect squares are numbers whose square roots are whole integers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on.
Can you take the square root of a negative number?
Not within the real numbers. The square root of a negative number is an imaginary number, written using the imaginary unit i, where i = √(−1).
How do you find the nth root of a number?
The nth root of a number x equals x raised to the power of 1/n. For instance, the cube root (3rd root) of 27 is 27^(1/3) = 3.
How is a square root different from a cube root?
A square root asks what number times itself gives x (power of 1/2). A cube root asks what number times itself three times gives x (power of 1/3). Both are special cases of the nth root.