Square Root Calculator
The square root of a number x is a value r such that r² = x. Every positive number has two square roots: a positive (principal) root and a negative root. Only zero has a single square root: zero itself.
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Tip: To check your answer: square it. If r = √x, then r² should equal x exactly.
- 1Factor the number into prime factors
- 2Pair up identical prime factors
- 3Take one factor from each pair and multiply them
- 4Any unpaired factors stay inside the radical symbol
√144=1212 × 12 = 144
√2=1.41421…Irrational — cannot be simplified further
√0.25=0.50.5 × 0.5 = 0.25
√200=10√2√(100 × 2) = 10√2 ≈ 14.142
Square root of zero
√0 = 0. Zero is the only number whose square root equals itself.
Square root of a negative number
Not real — gives an imaginary number. √(−1) = i, the imaginary unit.
| n | n² | √(n²) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 2 |
| 3 | 9 | 3 |
| 4 | 16 | 4 |
| 5 | 25 | 5 |
| 6 | 36 | 6 |
| 7 | 49 | 7 |
| 8 | 64 | 8 |
| 9 | 81 | 9 |
| 10 | 100 | 10 |
| 11 | 121 | 11 |
| 12 | 144 | 12 |
| 13 | 169 | 13 |
| 14 | 196 | 14 |
| 15 | 225 | 15 |
| 16 | 256 | 16 |
| 17 | 289 | 17 |
| 18 | 324 | 18 |
| 19 | 361 | 19 |
| 20 | 400 | 20 |
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Fun Fact
The ancient Babylonians calculated square roots using a method equivalent to Newton's method around 1700 BC — over 3,500 years ago.
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