Updated Math & Algebra

Root Calculator

Calculate square roots, cube roots, nth roots, simplify radicals, handle complex roots, and solve xⁿ = k in one place.

Square Root Cube Root nth Root Radical Simplifier

All-in-One Root Calculator

Switch between square root, cube root, nth root, radical simplifier, complex roots, and equation root solver.

For negative x, the real square root does not exist; the result is shown as a complex number.

If x is negative and n is even, there is no real nth root.

The radical simplifier looks for the largest perfect square factor of n and rewrites √n = a√b.

This tab shows the principal complex nth roots using polar form; for n = 2 it displays the two square roots.

If k is negative and n is even, there is no real solution. For positive k and even n, the real roots are ±k^(1/n).

Root Calculator – Square Roots, Cube Roots, nth Roots and More

This Root Calculator brings together square roots, cube roots, nth roots, radical simplification, complex roots, and equation solving in one place. It is useful for algebra, precalculus, and general math problem solving.

Square Root and Cube Root

The Square Root tab calculates √x for any real number x. For positive x, the principal real root is returned. For negative x, the calculator shows that there is no real root but gives the complex result in the form bi. The Cube Root tab handles ∛x for positive and negative values, since cube roots of negative numbers are real.

nth Root

The nth Root tab calculates x^(1/n) for a number x and a root index n. When n is odd, negative values of x have a real nth root. When n is even, negative x has no real nth root, and the calculator reports this in the status field.

Radical Simplifier

The Radical Simplifier focuses on square roots of positive integers. It searches for the largest perfect square factor of n and rewrites:

√n = a√b

where a² divides n and b is the remaining factor under the radical. This is useful for simplifying radical expressions in algebra and trigonometry.

Complex Roots

The Complex Roots tab interprets a complex number a + bi in polar form and computes its nth roots. For n = 2, it shows the two square roots; for higher n, it displays the principal root and a general expression that reflects the pattern of all nth roots on the complex plane.

Solving xⁿ = k

The Equation tab solves equations of the form xⁿ = k for real roots. For positive k and odd n, there is one real root. For positive k and even n, there are two real roots, ±k^(1/n). If k is negative and n is even, there is no real solution.

Explore more free calculators on MyTimeCalculator for math, science, finance, health, and fitness to support your learning and planning.

Related Calculators