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Square Root Calculator

Square root, cube root and any nth root of a number.

By CalcHub Editorial · Last reviewed

Quick answer

  • Formula: √x = x^(1/2); nth root = x^(1/n)
  • Worked example — Square root (√): 12.0000 (full example below).

Square Root Calculator

Worked example result
Square root (√)12.0000
Cube root (∛)5.2415
Nth root12.0000

√144 = 12 exactly, because 144 is a perfect square (12²). Its cube root is about 5.2415, since 5.2415³ ≈ 144.

Diagram: how the Square Root Calculator works — you enter Number, Root degree (n) for the nth root; it applies the formula √x = x^(1/2); nth root = x^(1/n); and the worked example gives Square root (√): 12.0000.
How the Square Root Calculator works — the inputs, the formula, and a worked example (Square root (√): 12.0000).

The square root of a number is the value that, multiplied by itself, gives the number back: √144 = 12 because 12 × 12 = 144. Cube roots do the same with three multiplications, and nth roots generalize the idea.

Enter a non-negative number and a root degree. You get the square root, the cube root and the root of the degree you chose — handy for geometry, where side lengths come from areas and volumes via roots.

The formula

√x = x^(1/2); nth root = x^(1/n)

Worked example

√144 = 12 exactly, because 144 is a perfect square (12²). Its cube root is about 5.2415, since 5.2415³ ≈ 144.

Worked example for the Square Root Calculator: with Number 144, Root degree (n) for the nth root 2, the result is Square root (√): 12.0000; Cube root (∛): 5.2415.
The worked example, with the example values entered and the results they give.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

Which numbers have exact square roots?

Perfect squares: 1, 4, 9, 16, 25, 36 and so on. Every other non-negative number has an irrational square root — √2 ≈ 1.4142… continues forever without repeating.

Why can't I take the square root of a negative number here?

No real number squared gives a negative result, so square roots of negatives belong to the complex numbers (written with i). This calculator works in real numbers only and will ask for a non-negative input.

Category: Math calculators

Sources & methodology

This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.

Content last reviewed by CalcHub Editorial.

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