Root Calculator
Find the square root, cube root or any nth root of a number.
How to use the Root Calculator
- Enter the number.
- Enter which root you want — 2 for square root, 3 for cube root.
- Read the result and the verification.
nth root of x = x^(1/n)
About the Root Calculator
The nth root of a number is the value that, multiplied by itself n times, gives back that number — and it is really a power in disguise: the nth root of x equals x^(1/n). This calculator uses exactly that relationship, so a square root is x^(1/2) and a cube root is x^(1/3). It also shows the plain square and cube roots of your number and a verification line that raises the answer back to the nth power, confirming it returns to where you started.
Signs are the real subtlety. An even root — square, fourth, sixth — of a negative number has no real value, because nothing real multiplied by itself an even number of times can be negative, and the tool says so rather than inventing an answer. An odd root — cube, fifth — of a negative number is real and comes out negative: the cube root of −8 is −2, since (−2)³ = −8.
Roots undo powers, so they appear in geometry, standard deviations and growth rates. To go the other way and raise a number to a power, use the exponent calculator; to solve equations with an x² term, try the quadratic equation solver.
Frequently asked questions
How do I get a square root or cube root?
Enter your number and set the root to 2 for a square root or 3 for a cube root. Any whole number works, so 4 gives the fourth root and 5 the fifth. The result also lists the square and cube roots for reference.
Why is the even root of a negative number rejected?
Because it has no real value. Squaring any real number, positive or negative, gives a positive result, so nothing real squared can equal a negative number. The same holds for fourth, sixth and other even roots, so the tool reports there is no real answer.
Can I take the root of a negative number at all?
Yes, when the root is odd. The cube root of −8 is −2 because (−2)³ = −8, and the same works for fifth, seventh and other odd roots. Only even roots of negative numbers fall outside the real numbers.
How are roots and powers related?
They are inverse operations. Taking the nth root is the same as raising to the power 1/n, so the fifth root of 32 is 32^(1/5) = 2. That is exactly how this calculator works out every result.
What is the verification line for?
It raises your answer back to the nth power so you can see it returns to the number you started with. For instance, the square root of 16 is 4, and the check shows 4² = 16 — a quick confirmation the result is right.