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Root Calculator

Calculate square roots, cube roots, and nth roots. Includes step-by-step simplification and decimal approximations.

Calculate Root
Value (x)
Root (n)

Simplify Radical (√)

Simplify √
Result
√144
12
12² = 144 (exact)
FormValue
Perfect Squares & Cubes Reference

Perfect squares

Perfect cubes

Roots and Radicals

The nth root of x is the number y such that yⁿ = x. Written as ⁿ√x or x^(1/n). The square root (n=2) is the most common.

Simplifying Radicals

To simplify √72: find the largest perfect square factor. 72 = 36×2, so √72 = √36 × √2 = 6√2 ≈ 8.485.

Irrational Numbers

Most roots are irrational (cannot be expressed as a simple fraction). √2 ≈ 1.41421356… is one of the most famous irrational numbers, proved irrational by the ancient Greeks.