Calculate the nth root of any number (ⁿ√x). Supports even and odd roots, real roots, radical expressions, and step-by-step solutions.
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An nth root of a number x is a number r which, when raised to the power n, yields x: r^n = x. Here, n is a positive integer called the index or degree of the radical.
r = \sqrt[n]{x} \iff r^n = x, \quad \sqrt[n]{x} = x^{1/n}Taking the nth root is mathematically equivalent to raising the radicand to the power of 1/n.
Scenario: Find the 5th root of 32
Radicand: x = 32, Degree: n = 5
Search for r such that r⁵ = 32
Notice 2⁵ = 2 × 2 × 2 × 2 × 2 = 32
Result: ⁵√32 = 2
Yes! Because a negative number raised to an odd power remains negative, odd roots of negative numbers exist on the real number line (e.g. ∛(-27) = -3).
The index is the small number n sitting in the crook of the radical sign that specifies which root is being taken.
The nth root of x is identical to raising x to the reciprocal power: ⁿ√x = x^(1/n).
Convert radicals to fractional exponents with a common denominator, then multiply using exponent laws.
Calculate the square root of positive and negative numbers (√x). Provides radical simplification, perfect square check, and imaginary roots.
Calculate the principal real cube root of positive and negative numbers. Identifies perfect cubes, nearest integer roots, and complex conjugate roots.
Calculate any base raised to the power of n (x^n) for positive, negative, and fractional exponents with step-by-step exponent laws.