NumberTally Root Calculator
Find the nth root of any number: square roots, cube roots like ∛27 = 3, and higher roots, with the exact value, a simplified surd form, and a square-vs-cube comparison. Results update instantly. Free, no sign-up.
2 = square root, 3 = cube root, etc.
Advanced options
How Roots Work
The nth root of x is the number that gives x when multiplied by itself n times: ∛27 = 3 because 3 × 3 × 3 = 27. Roots are fractional exponents in disguise — the nth root of x is x1/n.
Negative numbers are special: odd roots of negatives are fine (∛−8 = −2, since −2 × −2 × −2 = −8), but even roots of negatives have no real answer — √−4 is imaginary. The calculator handles both cases and tells you which one you hit.
Simplifying Surds
Many roots are irrational, like √2 ≈ 1.41421. Mathematicians often leave them in simplified surd form by factoring out perfect squares: √50 = √(25 × 2) = 5√2. The results below show the simplified form whenever one exists, which is exact — unlike any decimal approximation.
Frequently Asked Questions
What is the cube root of 27?
3, because 3 × 3 × 3 = 27.
Can you take the square root of a negative number?
Not in real numbers — no real number squared gives a negative. Odd roots (cube, 5th) of negatives are fine, e.g. ∛−8 = −2.
What is √2 exactly?
It is irrational: 1.41421356… with no repeating pattern. It cannot be written as a fraction.
How do you simplify √50?
Factor out the largest perfect square: √50 = √(25×2) = 5√2.
What is the relationship between roots and exponents?
The nth root of x equals x^(1/n). So ∛27 = 27^(1/3) = 3.