What is a square root?

The square root of x is the number y such that y² = x. √64 = 8 because 8² = 64.

Can I take the square root of a negative number?

Not in real numbers. Even roots of negatives are complex. Odd roots of negatives are real: ∛(-8) = -2.

The nth root of x is the number y such that yⁿ = x. Equivalently, ⁿ√x = x^(1/n).

Root Calculator

Enter a number and a root degree n to compute the nth root instantly. Square root, cube root, and any nth root are covered, including negative radicands for odd-degree roots.

How to use this calculator

Enter the radicand x — the number under the root sign.
Enter the root degree n: 2 for square root, 3 for cube root, etc.
Read the result, plus square root and cube root shown as reference.

Formula & method

Nth root formula

ⁿ√x = x^(1/n) · Verification: (ⁿ√x)ⁿ = x

Negative radicand allowed only for odd n. n = 0 is undefined.

Example

∛64 = 64^(1/3) = 4 (verification: 4³ = 64). √144 = 12 (verification: 12² = 144).

Key insights

Square root (n = 2) is the most common root: √64 = 8 because 8² = 64.
Cube root (n = 3) is the only real odd root of a negative number: ∛(-8) = -2.
The nth root of x equals x^(1/n) — a fractional exponent.
Irrational numbers like √2 ≈ 1.41421 cannot be expressed as exact fractions.

How to interpret your result

Square root vs cube root

Square root undoes squaring (n = 2). Cube root undoes cubing (n = 3) and accepts negative inputs.

Even roots of negative numbers

Even-degree roots (n = 2, 4, 6, …) of negative numbers are complex and not supported here.

Frequently asked questions

What is a square root?: The square root of x is the number y such that y² = x. √64 = 8 because 8² = 64.
Can I take the square root of a negative number?: Not in real numbers. Even roots of negatives are complex. Odd roots of negatives are real: ∛(-8) = -2.
What is an nth root?: The nth root of x is the number y such that yⁿ = x. Equivalently, ⁿ√x = x^(1/n).

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