Nth Root Calculator (square, cube…)
Find the square root, cube root or any nth root of a number.
Result
Result
3.000000
How it works
The nth root asks the reverse of a power: which number, multiplied by itself n times, gives your input? The cube root of 27 is 3, because 3 × 3 × 3 = 27, and the calculator computes it as 27^(1/3). That exponent form is the key idea — a root simply is a fractional power. The square root is the power ½, the cube root the power ⅓, and this is why roots obey exactly the same algebraic rules as any other exponent, including combining as x^(m/n) = the nth root of x^m. Negative inputs behave differently by parity. Odd roots are fine: the cube root of −8 is −2, since (−2)³ = −8. Even roots of negatives have no real answer, because any real number squared is positive — which is exactly the gap that imaginary numbers were invented to fill.
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Frequently asked questions
What is the cube root of 27?
3, because 3 × 3 × 3 = 27.
Can I take the root of a negative number?
Only with an odd index (e.g. cube root of −8 = −2). Even roots of negatives have no real value.
What is the difference between a root and a fractional power?
There is none — they are two notations for the same operation. The nth root of x is x^(1/n), which is why a calculator with only a power key can compute any root you need.
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