Square Root Calculator
Find the square root, cube root or any other root of a number. For whole numbers you also get the simplified form, such as √72 = 6√2.
About this tool
Odd roots of negative numbers work (∛−27 = −3). Even roots of negative numbers have no real answer, and the tool says so instead of showing an error.
Find the square root of a number, or its cube root or any other root up to the 10th. For whole numbers the calculator also gives the simplified radical form, which is the answer most maths teachers want, and it tells you whether the number is a perfect square or cube.
How to use the Square Root Calculator
- Type the number, for example 72.
- Choose the root: square root, cube root or a higher root.
- Read the decimal answer, the simplified form and a check that raises the answer back to the power.
√72 and ∛54
√72 = 8.485281… . To simplify it, find the biggest perfect square that divides 72: 36. Then √72 = √(36 × 2) = 6√2. In the same way, ∛54 = ∛(27 × 2) = 3∛2, about 3.779763. The cube root of −27 is −3, because (−3)³ = −27.
Square roots of common numbers
Worked out with this calculator, to 6 decimal places.
| Number | Square root | Simplified |
|---|---|---|
| 2 | 1.414214 | √2 |
| 3 | 1.732051 | √3 |
| 8 | 2.828427 | 2√2 |
| 12 | 3.464102 | 2√3 |
| 18 | 4.242641 | 3√2 |
| 20 | 4.472136 | 2√5 |
| 50 | 7.071068 | 5√2 |
| 72 | 8.485281 | 6√2 |
| 98 | 9.899495 | 7√2 |
| 200 | 14.142136 | 10√2 |
What a root is
The square root of a number is the value that gives the number when multiplied by itself: √49 = 7 because 7 × 7 = 49. The cube root is the value that gives the number when used three times: ∛8 = 2 because 2 × 2 × 2 = 8. Every positive number has a positive square root, and also a negative one (−7 × −7 = 49 as well); calculators show the positive one. A negative number has no real square root, but it does have a real cube root.
Common mistakes
- Simplifying with a factor that isn’t the biggest perfect square. √72 = 2√18 is true but not fully simplified; 6√2 is.
- Adding roots as if they were ordinary numbers: √9 + √16 = 7, but √(9 + 16) = 5.
- Expecting a real square root of a negative number. √−4 is not a real number.
Frequently asked questions
What is the square root of 2?
About 1.414214. It never ends or repeats, because √2 is irrational.
How do I simplify a square root?
Split the number into a perfect square times something else, then take the root of the perfect square: √50 = √(25 × 2) = 5√2.
Can I find the root of a decimal?
Yes. √0.25 = 0.5. The simplified form is shown for whole numbers only.
What is the 10th root of 1,024?
2, because 2¹⁰ = 1,024.