Calculate square roots and squares instantly. Perfect for algebra, geometry, engineering, and everyday math problems.
Last updated: April 2026 | By Patchworkr Team
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 × 4 = 16.
The square root symbol is √. So √16 = 4. Every positive number has two square roots: one positive and one negative. This calculator returns the positive (principal) square root.
Perfect squares (like 1, 4, 9, 16, 25, etc.) have whole number square roots. Most other numbers have irrational square roots with infinite decimal places (like √2 ≈ 1.414...).
Square root reverses squaring. If you know the square, you can find the original number.
Multiply a number by itself to get its square.
These have exact whole-number square roots.
What number multiplied by itself gives 144?
| Number | Calculation | Square |
|---|---|---|
| 1 | 1² | 1 |
| 2 | 2² | 4 |
| 3 | 3² | 9 |
| 4 | 4² | 16 |
| 5 | 5² | 25 |
| 6 | 6² | 36 |
| 7 | 7² | 49 |
| 8 | 8² | 64 |
| 9 | 9² | 81 |
| 10 | 10² | 100 |
| 11 | 11² | 121 |
| 12 | 12² | 144 |
| 13 | 13² | 169 |
| 14 | 14² | 196 |
| 15 | 15² | 225 |
| 16 | 16² | 256 |
Not in real numbers. Square roots of negatives produce imaginary numbers (involving i).
√2 ≈ 1.414. It's an irrational number—its decimal never ends or repeats.
They appear in geometry, algebra, and provide easy reference points for estimating other square roots.
No. The square root symbol √ always means the positive root. √16 = 4 (not -4).
Find nearby perfect squares: 7² = 49 and 8² = 64, so √50 is between 7 and 8 (≈ 7.07).
They're inverses. If x² = y, then √y = x. Square root undoes squaring.
In real numbers, no. But in complex numbers, yes—they involve the imaginary unit i.
Technically two: one positive and one negative. The √ symbol typically refers to the positive root.
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