Square Root Calculator
Square roots, cube roots and any nth root.
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The square root of a number is the value that, multiplied by itself, gives that number. This calculator finds the square root by default, the cube root with one tap, and any nth root if you set the degree — with a check shown so you can confirm the answer.
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How to Find a Square Root — The Quick Answer
The square root of a number is what you multiply by itself to get that number (√144 = 12 because 12 × 12 = 144). A cube root uses three equal factors, and an nth root uses n of them. Taking a root is the opposite of raising to a power.
Shortcut
√x = x^(1/2) | ∛x = x^(1/3) | ⁿ√x = x^(1/n)
Common roots
| Root | Means | Result |
|---|---|---|
| √144 | what × itself = 144 | 12 |
| √2 | non-perfect square | 1.41421356… |
| ∛27 | what × itself × itself = 27 | 3 |
| ∛-27 | odd root of a negative | -3 |
| ⁴√81 | fourth root | 3 |
You can take an odd root (cube, 5th, …) of a negative number — ∛-27 = -3 — but not an even root, because no real number squared is negative. Even roots of negatives are 'imaginary', so they aren't defined here.
How It Works
The Method
Roots as fractional powers
Formula
ⁿ√x = x^(1/n) Square root: √x = x^(1/2) Cube root: ∛x = x^(1/3)
Variables
Square root
The value that multiplied by itself gives x. √144 = 12 because 12² = 144. Perfect squares (4, 9, 16, 25…) give whole-number roots; everything else gives a non-terminating decimal like √2 ≈ 1.41421356.
nth root
The value that, raised to the power n, gives x. It equals x raised to the power 1/n. The cube root of 27 is 3 because 3³ = 27; the fourth root of 81 is 3 because 3⁴ = 81.
Roots of negative numbers
Odd roots of negatives are real: ∛-27 = -3, since (-3)³ = -27. Even roots of negatives are not real numbers (nothing real squares to a negative), so they are reported as undefined here.
Note: Taking a root and raising to a power are inverse operations: (√x)² = x and (ⁿ√x)ⁿ = x. That relationship is exactly what the on-screen check confirms.
Worked Example
√144 and ∛27
√144
Find the number that multiplied by itself gives 144. 12 × 12 = 144, so √144 = 12.
∛27
Find the number used three times that gives 27. 3 × 3 × 3 = 27, so ∛27 = 3.
√2 (not a perfect square)
There's no whole number whose square is 2, so the root is an endless decimal: √2 ≈ 1.41421356.
Reference Guide
| unit | value | note |
|---|---|---|
| √144 | 12 | perfect square |
| √2 | 1.41421356 | irrational |
| ∛27 | 3 | cube root |
| ⁴√81 | 3 | fourth root |
Key Features
Last updated: October 5, 2026
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Frequently Asked Questions
What is a square root?
The square root of a number is the value that, multiplied by itself, gives that number. For example √144 = 12 because 12 × 12 = 144. Numbers like 4, 9, 16 and 25 are 'perfect squares' with whole-number roots; most numbers have an irrational square root that runs on forever, like √2 ≈ 1.41421356.
How do I find a cube root or nth root?
A cube root asks which number used three times gives your value (∛27 = 3 because 3 × 3 × 3 = 27). More generally, the nth root equals the number raised to the power 1/n. Set the degree to 3 for a cube root, 4 for a fourth root, and so on.
Can you take the square root of a negative number?
Not as a real number — no real number multiplied by itself gives a negative result, so √-9 is 'imaginary'. However, odd roots of negatives are real: the cube root of -27 is -3, because (-3)³ = -27. This calculator handles odd roots of negatives and flags even ones as undefined.
What's the difference between a root and a power?
They are inverse operations. Raising to a power multiplies a number by itself repeatedly; taking a root undoes that. Squaring 12 gives 144, and the square root of 144 gives 12 back. In fact a root is just a fractional power: √x is the same as x^(1/2).