√ Square Root Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Enter a number to see its square root and cube root.
This square root calculator takes any number you type and shows two results at once: its square root and its cube root. It works with whole numbers, decimals, and negatives. Because the square root of a negative number is not a real number, the calculator tells you so clearly, while still showing the cube root, which is always real.
What is the Square Root Calculator?
The square root of a number n is the value that, multiplied by itself, gives n. For example the square root of 144 is 12, because 12 times 12 equals 144. Every positive number has two square roots, one positive and one negative (12 and -12 both square to 144), but the symbol √ refers to the principal (non-negative) root, which is what this calculator reports. The square root of 0 is 0.
Negative numbers behave differently. No real number multiplied by itself gives a negative result, since a positive times a positive is positive and a negative times a negative is also positive. So the square root of a negative number has no real value; it belongs to the complex numbers, written using the imaginary unit i. This tool works with real numbers, so for a negative input it reports "Not real" for the square root.
The cube root of n is the value that, multiplied by itself three times, gives n. Cube roots are friendlier with negatives: because a negative times a negative times a negative is negative, the cube root of -27 is -3, a perfectly ordinary real number. That is why this calculator can always show a cube root even when the square root is undefined. Perfect squares (such as 1, 4, 9, 16, 25) and perfect cubes (such as 1, 8, 27, 64) give whole-number roots; most other numbers give irrational decimals that we round for display.
When to use it
- Checking homework or test answers for square and cube root problems.
- Finding the side length of a square from its area, or the edge of a cube from its volume.
- Working out the geometric mean of two numbers, or the standard deviation step that needs a square root.
- Confirming whether a number is a perfect square or perfect cube.
How to use the Square Root Calculator
- Type a number into the box (it can be a whole number, a decimal, or negative).
- Read the square root shown in the first result box.
- Read the cube root shown in the second result box.
- For a negative number, note that the square root reads "Not real" while the cube root is still shown.
Formula & method
Worked examples
Find the square root and cube root of 144.
- 144 is a perfect square: 12 × 12 = 144, so √144 = 12.
- Cube root: 5.24 × 5.24 × 5.24 ≈ 144, so ∛144 ≈ 5.241483.
Result: √144 = 12, ∛144 ≈ 5.241483
Find the square root of 2.
- 2 is not a perfect square, so its square root is irrational.
- 1.41421356 × 1.41421356 ≈ 2, so √2 ≈ 1.41421356.
Result: √2 ≈ 1.41421356
Find the square root and cube root of -27.
- A negative number has no real square root, so √(-27) is Not real.
- Cube root is fine with negatives: (-3) × (-3) × (-3) = -27, so ∛(-27) = -3.
Result: √(-27) = Not real, ∛(-27) = -3
Common square roots and cube roots
| Number (n) | Square root (√n) | Cube root (∛n) |
|---|---|---|
| 1 | 1 | 1 |
| 4 | 2 | 1.587401 |
| 8 | 2.828427 | 2 |
| 9 | 3 | 2.080084 |
| 16 | 4 | 2.519842 |
| 25 | 5 | 2.924018 |
| 27 | 5.196152 | 3 |
| 64 | 8 | 4 |
| 100 | 10 | 4.641589 |
| 144 | 12 | 5.241483 |
Common mistakes to avoid
- Expecting a real square root of a negative number. The square root of a negative number is not a real value, because no real number squared is negative. The answer lies in the complex numbers (using i). This calculator reports "Not real" for such inputs.
- Confusing the square root with halving. The square root of 16 is 4, not 8. Taking a square root is not the same as dividing by 2. √n asks which number times itself gives n.
- Forgetting the negative root exists. Both 5 and -5 square to 25. The √ symbol gives only the principal (non-negative) root, but when solving an equation like x² = 25 remember to include x = -5 as well.
Glossary
- Square root
- A value that multiplied by itself gives the original number. √25 = 5.
- Cube root
- A value that multiplied by itself three times gives the original number. ∛27 = 3.
- Principal root
- The non-negative square root, the one the √ symbol refers to.
- Perfect square
- A number whose square root is a whole number, such as 1, 4, 9, 16, or 25.
- Radicand
- The number under the root symbol, the value whose root you are finding.
- Imaginary unit (i)
- A symbol defined so that i × i = -1, used to express square roots of negative numbers.
Frequently asked questions
What is the square root of a number?
The square root of a number is the value that, multiplied by itself, gives that number. For example the square root of 144 is 12, because 12 times 12 equals 144.
Can you take the square root of a negative number?
Not as a real number. No real number squared gives a negative result, so the square root of a negative belongs to the complex numbers (written with i). This calculator reports "Not real" for negative inputs.
What is the difference between a square root and a cube root?
A square root finds the value that squares to your number (√25 = 5), while a cube root finds the value that cubes to it (∛27 = 3). Cube roots also work for negatives, since a negative cubed stays negative.
What is the cube root of a negative number?
It is a real negative number. Because a negative times a negative times a negative is negative, the cube root of -27 is -3. The calculator always shows the cube root, even for negative inputs.
Is the square root of 2 a whole number?
No. The square root of 2 is irrational, approximately 1.41421356, with digits that go on forever without repeating. Only perfect squares like 1, 4, 9, and 16 have whole-number square roots.
How accurate are the results?
Results use your browser’s built-in math and are rounded for display to several significant figures. For perfect squares and cubes you get exact whole numbers; for other values you get a precise decimal approximation.