Free online square root calculator

A square root is the number that, when multiplied by itself, gives the original value — √9 = 3 because 3×3 = 9. This calculator finds the nth root of any real number and shows.

Value

Root degree (nth)

2 = square root, 3 = cube root, etc.

How to use

Enter the value whose root you want.
Set the root degree — 2 for square root, 3 for cube root, etc.
The result and expression appear instantly.

The formula

nth root of x = x^(1/n)

For x < 0 and odd n:
  result = −(|x|^(1/n))

For x < 0 and even n:
  result is complex (not real) — error shown

Source: Stewart J. Calculus: Early Transcendentals. 8th ed. §1.5

Worked examples

√9 = 3 — 3² = 9 (perfect square)

√2 ≈ 1.41421356 — irrational, shown to 9 significant figures

∛27 = 3 — 3³ = 27 (perfect cube)

∛(−27) = −3 — (−3)³ = −27 (negative, odd root)

⁴√16 = 2 — 2⁴ = 16 (perfect fourth root)

Common perfect squares and cubes

Value	Square root	Cube root
1	1	1
4	2	—
8	—	2
9	3	—
16	4	—
25	5	—
27	—	3
64	8	4
125	—	5

Notes

The root degree must be a positive whole number.
Results are shown to 9 significant figures for irrational roots.
The square and cube values shown are the original value squared and cubed, not the result.

Frequently asked

What is an nth root?

The nth root of x is the number r such that r^n = x. The square root is n=2, the cube root is n=3, and so on. This calculator computes x^(1/n) for any positive integer n.

Can I take the square root of a negative number?

Not in the real numbers — the square root of a negative number is complex (imaginary). This calculator returns an error for even roots of negative values. Odd roots (like cube roots) of negative numbers are real and negative.

What is a perfect root?

A perfect root is one where the result is an exact integer. For example, √9 = 3 (perfect square), ∛27 = 3 (perfect cube). The calculator flags these with a "perfect root" label.

How is the nth root computed?

Using the power rule: nth root of x = x^(1/n). For negative x with odd n, the result is −(|x|^(1/n)).

What is the cube root of a negative number?

Odd roots of negative numbers are negative real numbers. For example, ∛(−27) = −3, because (−3)³ = −27.