Square Root and Nth Root Calculator

Calculate square roots, cube roots, and any nth root of a number with precision.

Square Root and Nth Root Calculator tool

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Example

Input: Square root of 50 (root degree n = 2)

Result: 7.0710678119 (not a perfect root)

sqrt(50) = sqrt(25 x 2) = 5 x sqrt(2) = 5 x 1.41421356 = 7.0710678119.

Square Roots and Cube Roots

NumberSquare rootCube root
21.41421356241.2599210499
31.73205080761.4422495703
52.23606797751.7099759467
82.82842712472
103.16227766022.15443469
275.19615242273
507.07106781193.6840314986
6484
100104.6415888336
100031.622776601710

Values from this calculator, rounded to 10 decimal places. Whole results are perfect roots.

  1. Enter the number (radicand) you want to find the root of.
  2. Enter the root degree n: 2 for square root, 3 for cube root, or any whole number up to 100.
  3. View the root displayed as a decimal with up to 10 decimal places.
  4. Check the perfect root indicator to see if the result is a whole number.
  5. Review the verification line, which raises the result back to the nth power.
  6. Click the copy button to copy any result.

Square Roots, Cube Roots and Perfect Squares

The square root of a number is the value that gives that number when multiplied by itself: the square root of 144 is 12. This calculator finds square roots, cube roots and any whole-number root up to the 100th. It tells you when the answer is a whole number, and it checks the result by raising it back to the power.

Roots come up in everyday problems. A square room of 200 square feet has sides of about 14.14 feet, the square root of 200. The diagonal of a right triangle is a square root too, which the Pythagorean Theorem Calculator works out for you. Cube roots turn a volume back into a side length: a 27-liter cube is 3 decimeters on each side.

You can estimate a square root in your head by finding the nearest perfect squares. The square root of 50 sits between 7 (49) and 8 (64), and much closer to 7, so it is about 7.07. The calculator gives 7.0710678119.

Negative numbers need care. An even root of a negative number, such as the square root of -9, has no real answer, so the tool shows an error. Odd roots are fine: the cube root of -27 is -3, because -3 x -3 x -3 = -27.

Results show up to 10 decimal places. The Perfect Root line says Yes when the answer is a whole number, as with 64, which is both 8 squared and 4 cubed. The nth root of x is the same as x to the power 1/n. For other powers, use the Exponent and Power Calculator.

Formula / How It Works

nth root of x = x^(1/n) | Square root of x = x^(1/2) | Cube root of x = x^(1/3)

Frequently Asked Questions

The square root of x is the number that gives x when multiplied by itself. The square root of 25 is 5, because 5 x 5 = 25. Every positive number also has a negative square root, here -5, but the usual square root means the positive one, and that is what the calculator shows.
A perfect square is a whole number whose square root is also a whole number. The first ten are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. The square root of any other whole number is irrational, so its decimal goes on forever without repeating.
Not in real numbers. No real number times itself gives a negative result. Mathematicians use the imaginary unit i, where i x i = -1, so the square root of -9 is 3i. This calculator works with real numbers, so it shows an error for even roots of negative numbers.
Cube roots of negative numbers are real and negative. The cube root of -27 is -3, because -3 x -3 x -3 = -27. The same is true for any odd root, such as a 5th root. Enter the negative number and an odd root degree, and the calculator returns the negative answer.
The nth root of x equals x raised to the power 1/n. So the square root of 16 is 16^0.5 = 4, and the cube root of 8 is 8^(1/3) = 2. This link lets you handle roots with the same rules you use for powers.

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