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Radical Calculator

Compute the nth root of any number or simplify a square root into its simplest radical form.

ⁿ√27
3
Even roots of negative numbers are undefined in the real numbers.

How it works

  1. 1In nth root mode, enter a value and a root index n; the calculator returns the real nth root via ⁿ√x = x^(1/n). Negative values work only when n is an odd integer.
  2. 2In Simplify √n mode, enter a non-negative integer; the tool extracts all perfect-square factors, expressing the result as coefficient·√radicand.
  3. 3Results update instantly as you type — no button press needed.

Use cases

  • Checking cube roots and higher-order roots in algebra or calculus homework.
  • Simplifying radical expressions before combining like terms or rationalising denominators.
  • Engineering and physics calculations that involve fractional exponents or root functions.

Frequently asked questions

Why does an even root of a negative number show —?

Even-index roots of negative numbers have no real solution — the result is a complex number. This calculator works in the reals only, so it returns — for those inputs.

What does simplest radical form mean?

A radical √n is in simplest form when the radicand has no perfect-square factor greater than 1. For example, √72 = √(36·2) = 6√2, so 6√2 is the simplest form.

Can I enter a fractional root index such as n = 1.5?

Yes — fractional n values are accepted in nth root mode. ⁿ√x is computed as x^(1/n), giving the principal real result.

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